On Global Stability of Financial Networks
%%%% First author details {{\sc Bhaskar DasGupta$^*$ }} \address{Department of Computer Science
Chicago
IL 60607
{Recent crisis in the global financial world has generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the ``financial contagion'' process in which insolvencies of individual entities propagate through the ``web of dependencies'' to affect the entire system. In this paper, we formalize an extension of a financial network model originally proposed by Nier \EA for scenarios such as the over-the-counter derivatives market, define a suitable global stability measure for this model, and perform a comprehensive evaluation of this stability measure over more than 700,000 combinations of networks types and parameter combinations. Based on our evaluations, we discover many interesting implications of our evaluations of this stability measure, and derive topological properties and parameter combinations that may be used to flag the network as a possible fragile network. An interactive software FIN-STAB for computing the stability is available from the website \url{www2.cs.uic.edu/~dasgupta/financial-simulator-files.}.} { Financial networks, financial contagion, global stability. } % \\ 2000 Math Subject Classification: 91B55, 91G99, 05C82.
paper-9-final.tex
\documentclass[numbib]{comnet}

\newcommand{\comment}[1]{}

\usepackage{pifont}
\usepackage{wrapfig}
\usepackage{longtable}
\usepackage{xspace}
\usepackage{url}
%%\usepackage{citesort}
%%\usepackage[numbers]{natbib}
\usepackage{afterpage} %% use \afterpage{\clearpage}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{nicefrac}
\usepackage{ctable} 
\usepackage{array} 
\usepackage{graphics,subfigure} 
\usepackage{pstricks,pst-plot,pst-coil,pst-text,multido,pst-3d,pst-tree,pst-grad,colortbl,color,multirow,booktabs}
\usepackage{pst-xkey,pst-solides3d} 
\usepackage{pst-3dplot} 

\newcommand{\textfrc}[1]{{\frcseries#1}}
\renewcommand{\thesubfigure}{(\Alph{subfigure})}
\newcommand{\EA}{{\em et al.}\xspace}
\newcommand{\IE}{{\em i.e.}\xspace}
\newcommand{\tx}{^{\rm th}}
\newcommand{\EG}{{\it e.g.}\xspace}
\renewcommand{\cite}{\citep}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% for removing extra default space for a figure in LaTex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% See p.105 of "TeX Unbound" for suggested values.
% See pp. 199-200 of Lamport's "LaTeX" book for details.
%   General parameters, for ALL pages:
\renewcommand\topfraction{.99}        % max fraction of floats at top
\renewcommand\bottomfraction{.99}     % max fraction of floats at bottom
\renewcommand\textfraction{.01}   
%   Parameters for TEXT pages (not float pages):
\setcounter{totalnumber}{2}
\setcounter{topnumber}{1}
\setcounter{bottomnumber}{1}
%   Parameters for FLOAT pages (not text pages):
\renewcommand{\floatpagefraction}{0.99}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

\title{On Global Stability of Financial Networks}

\shorttitle{Stability of Financial Networks}
\shortauthorlist{DasGupta and Kaligounder} %%% for verso running head

\author{%%%% First author details
{{\sc 
Bhaskar DasGupta$^*$
}}
\address{Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA\email{$^*$Corresponding author: bdasgup@uic.edu}}
%%%%%%% Second author details
\and
{{\sc 
Lakshmi Kaligounder
}}
\address{Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA} 
}

\maketitle

\begin{abstract}
{Recent crisis in the global financial world has generated renewed interests in fragilities of global financial networks
among economists and regulatory authorities.
In particular, a potential vulnerability of the financial networks is the ``financial contagion''
process in which insolvencies of individual entities propagate through the ``web of dependencies'' to affect
the entire system. In this paper, we formalize an extension of a financial network model originally proposed by Nier \EA
for scenarios such as the over-the-counter derivatives market,
define a suitable global stability measure for this model, and perform a comprehensive evaluation of this stability measure 
over more than 700,000 combinations of networks types and parameter combinations. Based on our evaluations, we 
discover many interesting implications of our evaluations of this stability measure, and
derive topological properties and parameter combinations that may be used to flag the network as a possible fragile 
network. An interactive software FIN-STAB for computing the stability is available from the website 
\url{www2.cs.uic.edu/~dasgupta/financial-simulator-files.}.}
{
Financial networks, financial contagion, global stability.
}
%
\\
2000 Math Subject Classification: 91B55, 91G99, 05C82.
\end{abstract}

\section{Introduction}

Recent unprecedented level of global financial crisis has clearly
exposed potential weaknesses of the global economic system, renewing interests in the 
determination of fragilities of various segments of the global economy. 
Since financial institutions governed by borrowing, lending and participation in risky investments
played a crucial role in this crisis, 
they have attracted a major part of the attention of economists; see~\cite{HM11} for a survey.
The issue of instability of free market based financial systems is not new and has been under
discussion among the economists starting with the early works of~\cite{F33,K36} during the 1930's great depression era.
However, the exact causes of such instabilities have {\em not} been unanimously agreed upon yet.
Economists such as Ekelund and Thornton~\cite{ET08} contend that a major reason for the recent financial crisis is 
the enactment of an act that removed several restrictions on mixing investment and consumer banking, 
whereas other economists such as Calabria disagree with such an assertion~\cite{C09}.
Some economists such as Minsky have argued that such instabilities are 
are {\em systemic} for many modern market-based economic systems~\cite{M77}. 

One motivation in this paper to investigate global stabilities of financial 
networks comes from the point of view of a {\em regulatory agency} (as was also the case, for example, 
in~\cite{HM11}). A regulatory agency with 
sufficient knowledge about a part of a global financial network is expected to periodically evaluate
the stability of the network, and flag the network {\em ex ante} for further analysis if it fails some preliminary 
test or exceeds some minimum threshold of vulnerability. In this motivation, 
flagging a network as vulnerable does not necessarily imply 
that such is the case, but that such a network requires further analysis based on other aspects of free market economics 
that are not or simply {\em cannot} be 
modeled\footnote{For example, some such factors are the {\em rumors} and {\em panics} caused by the insolvency
of a large bank and a possible subsequent credit freeze. While fears, panics and rumors are all real aspects in networked economics,
there are hardly any universally agreed upon good way of modelling them.}.
While too many false positives may drain the finite resources of a regulatory agency for further analysis and investigation, 
this motivation assumes that vulnerability is too important an issue to be left for an {\em ex post} analysis.

Similar to prior research works such as~\cite{arxiv,E04,HM11,NYYA07,GK08,MA10},
our study of the vulnerability of financial networks also assumes the absence of government intervention
as banks become insolvent. 
%
While this is an extreme worst-case situation, the main goal of such type of studies is to see if the network can survive 
a shock even under extreme situations. A further reason for not allowing any intervention is, unlike the case of public health issues such as controlling spread of epidemics, 
government intervention in a capitalist financial system is often not allowed or requires complex political and administrative operatives. 












\section{Brief review of related prior works on financial networks}

Although there is a large amount of literature on stability of financial systems 
(\EG, see~\cite{E04,arxiv,FN09,B07,Ace2013,E2013,PYR09,MR13,La13,AG2000,DP83,GK08,XBJ2000,H09,Lie2010,D04,RS98,CM09,NYYA07,CD09,A05}), 
very few prior papers have mathematically defined a global stability measure and 
performed a comprehensive evaluation of such a measure as done in this paper. A most recent research work related to our work is the paper by 
Minoiu and Reyes~\cite{MR13} in which the authors analyzed global banking networks data on cross-border banking flows for 184 countries during 1978-2010
using local connectivity and clustering measures. Below we review other related prior research works. 
Although ordinarily one would expect the risk of contagion to be larger in a highly interconnected banking system, 
prior simulation works indicate that higher connectivity among banks may sometimes lead to lower risk of contagion.
{\em Due to the large volume of prior research works,
we are only able to review a selected subset of related prior research works, leaving many other exciting research results in the bibliographies of the 
cited papers}. 

Allen and Gale~\cite{AG2000} found that when consumers have the liquidity preferences as introduced by Diamond and Dybvig~\cite{DP83} and have 
random liquidity needs, banks {\em perfectly} insure against liquidity fluctuations by exchanging interbank deposits, but the connections created by 
{\em swapping deposits} expose the {\em entire system} to contagion. 
Based on such studies, Allen and Gale~\cite{AG2000} concluded that incomplete networks are {\em more} prone to contagion than networks with maximum connectivity since 
better-connected networks are more resilient via transfer of proportion of the losses in one bank's portfolio to more banks through interbank agreements. 
On the other hand, Gai and Kapadia~\cite{GK08} argued that the higher is the connectivity among banks the more will be the contagion effect during crisis. 
Freixas \EA \cite{XBJ2000} explored the case of banks that face liquidity fluctuations due to the uncertainty about 
consumers withdrawing funds. 
Haldane~\cite{H09} suggested that contagion should be measured based on the interconnectedness of each institution within the financial system.
Liedorp \EA~\cite{Lie2010} argued that both large lending and borrowing shares in interbank markets increase the riskiness of banks active in the {\em dutch} banking market. 

Dasgupta~\cite{D04} explored how linkages between banks, represented by cross-holding of deposits, can be a source of contagious breakdowns by investigating 
how depositors, who receive a private signal about fundamentals of banks, may want to withdraw their deposits if they believe that enough other depositors will do the same. 
Lagunoff and Schreft~\cite{RS98} studies a network model in which the return on an agents' portfolio depends on the portfolio allocations of other agents.  
Iazzetta and Manna~\cite{CM09} used network topology analysis on monthly data on deposits exchange to gain more insight into the way a liquidity crisis spreads. 
Nier \EA~\cite{NYYA07} explored the dependency of systemic risks on the structure of the banking system 
and the resilience (or lack thereof) of such a  system to contagious defaults via graph theoretic approach.
Corbo and Demange~\cite{CD09} explored the relationship of the structure of interbank connections to the contagion risk of defaults
given the exogenous default of set of banks.
Babus~\cite{A05} studied how the trade-off between the benefits and the costs of being linked changes depending on the network structure, and 
observed that, when the network is maximal, liquidity can be redistributed in the system to make the risk of contagion minimal. 

%
Acemoglu \EA~\cite{Ace2013} and Zawadowski~\cite{Z11} do investigate stability of financial networks, but differently from our study. Both~\cite{Ace2013} and~\cite{Z11}
consider two specific network topologies, namely the ring topology and the complete network topology, as opposed to a more general class of topologies in our study. 
Both~\cite{Ace2013} and~\cite{Z11} consider only the effect of the shock propagation for {\em a few} discrete time steps, as opposed to our study; 
in the terminology of~\cite{arxiv}, this can be thought of as a ``violent death'' of the network as opposed to the ``slow poisoning death'' that our paper investigates. 
The model and structure/terms of bilateral interbank agreements in~\cite{Ace2013}, namely that banks lend to one another through debt contracts with contingency covenants, 
is quite different from ours. As a results, the conclusions in~\cite{Ace2013,Z11} do not directly apply to our model and the corresponding simulation environment.

Attribute propagation models have been investigated in the past in other contexts such as influence maximization in social networks~\cite{kempe1,CWY09,Chen08,borodin}, 
disease spreading in urban networks~\cite{eubank04,coelho08,eubank05}, and percolation models in physics and mathematics~\cite{SA94}. 
However, the shock propagation model in this paper is very different from all these models. For example: 
%
\begin{itemize}
\item
Almost all of the other models include a trivial solution in which the attribute spreads to the entire network if we inject each node individually with the attribute. 
This is not the case with the shock propagation model.

\item
If shocking a subset of nodes makes $x$ nodes in the network fail, then adding more nodes to this subset may not necessarily lead to the failure of $x$ or more than $x$ nodes of the network.

\item
The complexity of many previous attribute propagation models arises due to the presence of cycles in the graph. 
In contrast, the shock propagation model may be highly complex {\em even when the given network is acyclic}. Instead, 
a key component of the complexity arises due to two or more directed paths sharing a node.
\end{itemize}
%



















\section{Organization of the paper}

The rest of the paper is organized as follows:

\vspace*{0.1in}
\noindent
{\large $\bullet$} $\,$ 
In Section~\ref{model-sec} we describe the network model and the corresponding stability measure. In particular:
%
\begin{itemize}
\item
In Section~\ref{s1} we define the balance sheet equations, and the two (homogeneous and heterogeneous) versions of our model
that provide an appropriate formalization and extension of the basic prior model of~\cite{E04,NYYA07}.

\item
In Sections~\ref{s2}--\ref{s3}, we provide formalizations of how the initial failures of some nodes in the network (\IE, a shock) 
originate, and how such failures are propagated to other network nodes in successive time steps using a discrete-time {\em shock propagation equation}.

\item
In Section~\ref{stab-def} we define our global network stability measure $\mathcal{K}$.

\item
In Sections~\ref{rat1}~and~\ref{rat2}, we provide rationales for the network model and the global stability measure, respectively.
\end{itemize}

\vspace*{0.1in}
\noindent
{\large $\bullet$} $\,$ 
In Section~\ref{sim-sec} we describe our simulation environment and the combinations of parameters that are being explored. In particular:
%
\begin{itemize}
\item
In Section~\ref{topo}, we discuss the random network models for generation of network topologies.

\item
In Section~\ref{shock-def} we state and justify the two modes of initial failures ({\em idiosyncratic} and {\em coordinated}) that are being used in the simulation.

\item
In Sections~\ref{alphabeta-sec}--\ref{para}, we describe the combinations of parameters used for homogeneous and heterogeneous networks 
and few other minor details of the simulation environment.
\end{itemize}

\vspace*{0.1in}
\noindent
{\large $\bullet$} $\,$ 
In Section~\ref{empiri-sec} we discuss our findings from the evaluation of the stabilities of the networks. In particular:
%
\begin{itemize} 
\item
Our six conclusions 
%
\scalebox{1.5}[1.5]{\ding{172}}--\scalebox{1.5}[1.5]{\ding{177}}
%
for the stability measure involving various combinations of 
network topology and parameters appear in Sections~\ref{jj1}--\ref{jjj1}. 


\item
In Section~\ref{kk2} we discuss two phase transition properties of the stability measure with an intuitive explanation for one of them.
\end{itemize}
%
Though the issue of stability of financial systems has been discussed by prior 
researchers~\cite{E04,arxiv,FN09,B07,Ace2013,E2013,PYR09,MR13,La13,AG2000,DP83,GK08,XBJ2000,H09,Lie2010,D04,RS98,CM09,NYYA07,CD09,A05}, 
no prior paper has performed a comprehensive evaluation of a global stability measure 
as done in this paper.

\section{Economic policy implications}
\label{econ-motiv}

Returning to our original motivation of flagging financial networks for potential vulnerabilities, 
our results suggest that a network model similar to that used in the paper may be flagged 
for the following cases: 
%
\begin{itemize}
\item
the equity to asset ratios of most banks are low, 

\item
the network has a highly skewed distribution of external assets and inter-bank exposures among its banks and 
the network is sufficiently sparse, 

\item
the network does not have either a highly skewed distribution of external assets or 
a highly skewed distribution of inter-bank exposures among its banks, but the network is sufficiently dense.
\end{itemize}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% introduction ends; model description starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Our financial network model and stability measure}
\label{model-sec}

\newcommand{\din}{{\mathrm{deg^{\,in}}}}
\newcommand{\dout}{{\mathrm{deg^{\,out}}}}
\newcommand{\dave}{{\mathrm{deg_{\,ave}}}}
\newcommand{\vdead}{{V_{\mathrm{\text{\bf\large\ding{34}}}}}}
\newcommand{\bank}{\mathrm{Bank}}
\newcommand{\E}{\mathcal{E}}
\newcommand{\I}{\mathcal{I}}
\newcommand{\R}{{\mathbb R}}
\newcommand{\vs}{{V_{{\text{\footnotesize\ding{54}}}}}}
\newcommand{\ex}{{\mathbb E}}
\newcommand{\Var}{{\mathrm{Var}}}
\newcommand{\A}{{\mathbb A}}
\newcommand{\B}{{\mathbb B}}
\newcommand{\cD}{{\mathcal{D}}}
\newcommand{\e}{{\mathrm{e}}}

Since our model has a large number of parameters, for the benefit of the reader we have included a 
short definition for major parameters at the beginning of each subsection where they are used.


\subsection{Network model and balance sheet}
\label{s1}

\begin{table}[htbp]
\begin{center}
\renewcommand{\tabcolsep}{2pt}
\begin{tabular}{r l  |  r l  |  r l}
\hline
\multicolumn{6}{c}{
A list of major parameters used in this section
}
\\
\hline
$\E$ & total external asset & $\I$ & total inter-bank exposure & $\gamma$ & ratio of equity to asset
\\
\hline
\begin{tabular}{c}
$w(e)$ 
\\
$=$
\\
$w(u,v)$ 
\end{tabular}
& 
\begin{tabular}{c}
weight of edge 
\\
$e=(u,v)$
\end{tabular}
& $\iota_v$ & interbank asset &
$e_v$ & \begin{tabular}{l}
           effective share of
           \\
           total external asset
        \end{tabular}
\\
\hline
$a_v$ & total asset & $b_v$ & 
          \begin{tabular}{l}
            total 
            interbank 
            borrowing
\end{tabular}
&
$c_v$ & net worth (equity)
\\
\hline
\end{tabular}
\renewcommand{\tabcolsep}{6pt}
\end{center}
\end{table}

\vspace*{0.1in}
\noindent
We state a formalization of an {\em ex ante} financial network model
similar to what has been used by researchers from Bank of England and elsewhere~\cite{E04,HM11,NYYA07,GK08,MA10}. 
As was done by these prior researchers, 
we formulate our model in terms of balance-sheet ``insolvency cascades'' in a
network of financial institutions ({\em hereafter simply called ``banks'' and ``banking networks''}) with {\em interlinked} balance sheets, where losses flow into the
asset side of the balance sheets. The same formulation can be used to analyze cascades of
cash-flow insolvency in {\em over-the-counter derivatives markets}. From now on, we will refer to balance-sheet insolvency simply as insolvency.

The banking network is represented by a {\em parameterized} node-weighted and edge-weighted directed graph $G=(V,E,\Gamma)$ in the following 
manner\footnote{The parameters $\E$, $\I$, $A$,  $\gamma$ and $\Phi$ were also used by prior researchers, and the parameters 
$\sigma_v$ and $w(e)$ are generalizations of parameters used by prior researchers.}:  
%
\begin{itemize}
\item
$\Gamma=\left\{\E,\I,\gamma\right\}$ is the set of parameters where 
%
\begin{itemize}
\item
$\E\in\R$ is the total external asset,

\item
$\I\in\R$ is the total inter-bank exposure,

\item
$A=\I+\E$ is the total asset, and 

\item
$\gamma\in(0,1)$ is the ratio of equity to asset.
\end{itemize}
%

\item
$V$ is the set of $n$ banks where 
%
\begin{itemize}
\item
the node weight $\sigma_v\in[0,1]$ denotes the share of total external asset for each bank $v\in V$ 
$\big(\sum_{v}\sigma_v=1\big)$. 
\end{itemize}
%

\item
$E$ represents the set of $m$ direct inter-bank exposures where 
%
\begin{itemize}
\item
$w(e)=w(u,v)>0$ is the weight of a directed edge $e=(u,v)\in E$.
\end{itemize}
%
\end{itemize}
%

\renewcommand{\tabcolsep}{6pt}
\begin{table}[htbp]
%
\caption{Relevant balance sheet details of a node $v$ in the network~\cite{E04,NYYA07,arxiv}.
The total amount of external assets $\E$ is assumed to be large enough such that $b_v-\iota_v+\sigma_v \, \E$ is positive.}
%
\label{balsheet}
%
\begin{center}
\begin{tabular}{l | l} 
\hline
\noalign{\smallskip}
\multicolumn{1}{c|}{\bf Assets} & \multicolumn{1}{c}{\bf Liabilities} 
\\
\hline
\noalign{\smallskip}
%
{
\begin{tabular}{rl}
$\iota_v=\sum_{(v,u)\in E} w(v,u)$ & \hspace*{0.05in} interbank asset 
\\
[0.15in]
$e_v=b_v-\iota_v+\sigma_v \, \E$ & 
            \begin{tabular}{l}
               effective share of
               \\
               total external asset
             \end{tabular}
\\
[0.15in]
$a_v=b_v+\sigma_v \E$ & \hspace*{0.05in} total asset
\end{tabular}
}
&
\begin{tabular}{rl}
$b_v=\sum_{(u,v)\in E} w(u,v)$ & 
\begin{tabular}{l}
            total 
            interbank 
            \\
            borrowing
\end{tabular}
\\
[0.15in]
$c_v=\gamma\,a_v$ & \hspace*{0.05in} net worth (equity)
\end{tabular}
\\
\noalign{\smallskip}
\hline
%
\end{tabular}
\end{center}
%
\end{table}
\renewcommand{\tabcolsep}{6pt}

The (interlocked) balance sheet for each node (bank) $v\in V$ is shown in Table~\ref{balsheet}.
Two types of banking network models are considered: 
%
\begin{description} 
\item[\bf Homogeneous model:]
$\E$ and $\I$ are {\em equally} distributed among the nodes and the edges, respectively, \IE, $\sigma_v=\frac{1}{n}$ for every node $v$, 
and $w(e)=\frac{\I}{m}$ for every edge $e$.

\item[\bf Heterogeneous model:]
$\E$ and $\I$ are not necessarily equally distributed among the nodes and the edges, respectively.
\end{description}
%
{\em Both} homogeneous and heterogeneous network models are relevant in practice, and have been investigated by prior researchers
such as~\cite{arxiv,HM11,NYYA07,AW12,GK08,MA10}.

\subsection{Initial insolvency via shocks}
\label{s2}

\renewcommand{\tabcolsep}{2pt}
\begin{tabular}{r l  |  r l  |  r l}
\hline
\multicolumn{6}{c}{
A list of major parameters and definitions used in this section
}
\\
\hline
$\vs$ & set of initially shocked nodes & $\Phi$ & severity of initial shock & $t$ & time variable
\\
\hline
shocking mechanism: & \begin{tabular}{l} 
                         rule to select an initial subset
                           \\
                         of nodes to be shocked 
                      \end{tabular}
& 
\\
\hline
\end{tabular}
\renewcommand{\tabcolsep}{6pt}

\vspace*{0.1in}
The initial insolvencies of a banking network at time $t=0$ are caused by ``shocks'' received by a {\em subset} $\emptyset\subset\vs\subseteq V$ of nodes. 
Such shocks can occur, for example, due to {\em operational risks} (\EG, frauds\footnote{Iyer and Peydro~\cite{IP06} show that
fraud is an important cause of bank insolvency.}) or {\em credit risks},
and has the effect of {\em reducing} the external assets of an {\em selected} subset of 
banks\footnote{Nier \EA~\cite{NYYA07} considered shocking only one (or a few) bank and empirically studying the effect of the shock on the entire network.
Berman \EA~\cite{arxiv}, on the other hand, analyzed the computational complexity issues of the 
problem of selecting a subset of nodes such that shocking them will make the network fail.}.
Mathematically, the effect of the initial shock is to {\em simultaneously} decrease the external assets of each shocked node $v\in\vs$ 
from $e_v$ by $s_v=\Phi\,e_v$, thereby reducing the net worth of $v$ from its original value $c_v$ to $c_v-s_v$,
where $(0,1]\ni\Phi>\gamma$ is a parameter denoting the {\em severity} of the initial shock.

In the rest of the paper, by the phrase ``shocking mechanism'', we refer to the {\em rule} that is used to select the initial subset of nodes to be 
shocked\footnote{Shocking mechanisms were not formally defined by prior researchers, but it was often implicit in their discussions.}.

\subsection{Insolvency propagation equation}
\label{s3}

\renewcommand{\tabcolsep}{4pt}
\begin{tabular}{r l  |  r l  }
\hline
\multicolumn{4}{c}{
A list of major parameters used in this section
}
\\
\hline
$\din(v)$ & in-degree of node $v$ & $\vdead\left(t,\vs\right)$ & 
         \begin{tabular}{l}
           set of nodes that became insolvent before time $t$ 
           \\
           when initial shock is provided to nodes in $\vs$ 
         \end{tabular}
\\
\hline
\end{tabular}
\renewcommand{\tabcolsep}{6pt}

\vspace*{0.1in}
Let the notation $\din(v)$ denote the in-degree of node $v$. 
The insolvencies propagate in {\em discrete} time units $t=0,1,2,\dots$; 
we add ``$\left(\dots,t,\vs,\dots\right)$'' to all relevant variables to indicate their dependences on $t$ and on the set $\vs$ of initially shocked 
nodes.
A bank becomes insolvent if its modified net worth becomes {\em negative}, and such a bank is {\em removed} from the network in the next time step. 
Let $\vdead\left(t,\vs\right)\subseteq V$ denote the set of nodes that became insolvent {\em before} time $t$ when an initial shock is 
provided to the nodes
\footnote{Thus, in particular, $\din\left(v,t,\vs\right)$ is the in-degree in the graph induced by the nodes in 
$V\setminus \vdead\left(t,\vs\right)$.}
in $\vs$. The insolvencies of banks at 
time $t$ affect the equity of other banks in the network at the next time step $t+1$ by the following {\em non-linear} ``insolvency propagation 
equation''$^{\,}$\footnote{An equation of same flavor with some simplification and omitted details was described in words by 
Nier \EA~\cite{NYYA07} and Eboli~\cite{E04}.}$^,$\footnote{Equation~\eqref{eq1} is highly non-linear. The results in~\cite{arxiv} indicate that {\em in general} it is 
{\sf NP}-hard to find a subset $\vs$ of initially shocked nodes such that 
$\displaystyle \left|\,\lim_{t\to\infty}\vdead\left(t,\vs\right)\,\right|$ is exactly or approximately maximized.}: 
%
\begin{gather}
\forall\,u\in V\setminus \vdead\left(t,\vs\right)
\colon
c_u\left(t+1,\vs\right) = c_u\left(t,\vs\right) \,\,\,\scalebox{2.5}[1]{\bf -}
\hspace*{-0.4in}
\sum_{v \, \pmb{\colon} \!\!\!\!\! \substack{\big( c_v\left(t,\vs\right)<0 \big) \\ \,\,\,\,\,\,\,\, \bigwedge \big( v\,\in V\setminus \vdead\left(t,\vs\right) \big) \\ \hspace*{-0.3in} \bigwedge \big( (u,v)\in E \big) } } 
\hspace*{-0.3in}
\frac{\min\Big\{\,\left|\,c_v\left(t,\vs\right)\,\right|\,,\,\,b_v\,\Big\}}{\din\left(v,\,t,\vs\right)}
\label{eq1}
\end{gather}
%
In Equation~\eqref{eq1}, the term $\dfrac{\left|\,c_v\left(t,\vs\right)\,\right|}{\din\left(v,t,\vs\right)}$ ensures the loss of equity of an insolvent bank to be distributed 
equitably among its creditors that have not become insolvent yet, whereas
the term $\dfrac{b_v}{\din\left(v,t,\vs\right)}$ ensures that the total loss propagated cannot be more than 
the total interbank exposure of the insolvent bank; see {\sc Fig}.~\ref{shock-eqn-fig} for a pictorial illustration.
The insolvency propagation continues until {\em no} new bank becomes insolvent. 
For notational convenience, we may use 
$\left(\dots,t,\dots\right)$
instead of 
$\left(\dots,t,\vs,\dots\right)$
when $\vs$ is clear from the context or is irrelevant.


\begin{figure*}
%
\includegraphics[width=1\textwidth]{shock-eqn-fig.eps}
%
\caption{Pictorial illustration of the shock transmission equation for a node $v$ from time $t$ to time $t+1$.}
%
\label{shock-eqn-fig}       
%
\end{figure*}






\subsection{Rationale for the network model and insolvency propagation equation}
\label{rat1}

As prior researchers~\cite{NYYA07,AG08,PYR09} have commented:
%
\begin{description}
\item
\hspace*{0.05in}
\em 
``conceptual frameworks from the theory of weighted graphs
with additional parameters may provide a powerful tool for analysis of banking network models''.
\end{description}
%
Several parametric graph-theoretic models, differing in the way
edges are interpreted and additional parameters are used to characterize the contagion,
have been used by prior researchers in 
finance and banking industry to study various research questions involving financial 
systems~\cite{arxiv,E04,HM11,AW12,NYYA07,F03,UW04,M07,ACM11,CMS10,SM12,Z11}.
As noted by researchers in~\cite{NYYA07,ACM11}:
%
\begin{description}
\item
\hspace*{0.05in}
\em 
``the modelling challenge in studying banking networks lies not so much in analyzing a model that is flexible enough to represent all types of insolvency cascades, but in 
studying a model that can mimic the empirical properties of these different types of networks''.
\end{description}
%
The insolvency propagation model formalized and evaluated in this paper using a mathematically precise abstraction
is similar to or a generalization of the models in~\cite{arxiv,E04,HM11,NYYA07,AW12,GK08,MA10,ACM11} that represent {\em cascades} of cash-flow insolvencies.
As~\cite{ACM11} observes, over-the-counter (OTC) derivatives and similar markets are {\em prone to this type of cascades}.
In such markets parties deal {\em directly} with one another rather than passing through an exchange, and thus 
each party is subject to the risk that the other party does not fulfill its payment obligations. 
The following example from~\cite{ACM11} illustrates chains of such interactions:
%
\begin{description}
\item
\hspace*{0.05in}
\cite{ACM11}\em
``Consider two parties A and B, such that A has a
receivable from party B upon the realization of some event. If B does not dispose of enough
liquid reserves, it will default on the payment. Now consider that B has entered an off-setting
contract with another party C, hedging its exposure to the random event. If C is cash-flow
solvent, then the payment will flow through the intermediary B and reach A. However, if C
is cash-flow insolvent and defaults, then the intermediary B might become cash-flow insolvent
if it depends on receivables from C to meet its payment obligations to A''.
\end{description}
%
The length of such chains of interactions in some OTC markets, like the {\em credit default swap market}, is {\em significant}~\cite{C10,MMM11}, 
thereby {\em increasing} the probability of cascade of cash-flow insolvencies~\cite{AG08}.
As~\cite{NYYA07} observes, an insolvency propagation model such as the one studied here
%
\begin{description}
\item
\hspace*{0.05in}
\em 
``conceptualises the main characteristics of a financial system using network theory
by relating the cascading behavior of financial networks both to the local properties of the nodes and to the underlying topology of the network, 
allowing us to vary continuously the key parameters of the network''.
\end{description}
%
Although the cascading effect studied is of somewhat special and simplified nature, as noted by~\cite{HM11}:
%
\begin{description}
\item
\hspace*{0.05in}
\em
``This is a deliberate oversimplification, aimed at a clearer understanding of how an initial failure can propagate shocks throughout the system''.
\end{description}










\subsection{A measure of global stability\protect\footnote{A mathematically precise definition of global stability measure was omitted by most prior researchers.}}
\label{stab-def}

\begin{table}[htbp]
\begin{center}
\renewcommand{\tabcolsep}{2pt}
\begin{tabular}{r l  |  r l  }
\hline
\multicolumn{4}{c}{
A list of major parameters used in this section
}
\\
\hline
$\Upsilon$ & a shocking mechanism & 
$\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right)=x$ & 
\begin{tabular}{p{3in}}
on an average $100x\%$ nodes of the network become insolvent with the given values of $\gamma$ and $\Phi$ 
if we provide an initial shock to a random subset of $100\mathcal{K}\%$ of nodes selected using the shocking mechanism $\Upsilon$
\end{tabular}
\\
\hline
\end{tabular}
\renewcommand{\tabcolsep}{6pt}
\end{center}
\end{table}










Consider a banking network model as described in Sections~\ref{s1}--\ref{s3}. Let $\mathcal{K}\in (0,1]$ be a real 
number\footnote{$\mathcal{K}$ is a new parameter not used by prior researchers.}
%
denoting the fraction of nodes in $V$ that received the initial shock under a shocking mechanism $\Upsilon$ 
and let $S_{\Upsilon,\mathcal{K}}$ be the set of all 
%
possible $(\mathcal{K}n)$-element subsets of $V$. 
%
The {\em vulnerability index}\footnote{Although simple topological properties such as clustering coefficients have been used by authors to study 
properties of networks~\cite{OKK04,SOKK}, they are too simplistic for stability analysis of financial networks.}
of the network is then defined as\footnote{In this definition, we implicitly assume that the shocking mechanism $\Upsilon$ allows one to 
select at least one set of $\mathcal{K}n$ nodes for the initial shock. Otherwise, we define $\xi$ to be zero.} 
%
\[
\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right)
=\frac{1}{n} \times 
\,
\ex \left[ \,\,\, \left|\,\lim_{t\to\infty}\vdead\left(t,\vs\right)\,\right| \, 
\,\colon \,
\text{
$\vs$ is selected randomly from $S_{\Upsilon,\mathcal{K}}$
}
\right]
\]
%
In the above definition, the $\frac{1}{n}$ factor is only
for a min-max normalization~\cite{HK00} to ensure that
$0\leq\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right)\leq 1$.
Noting that no new node in the network may fail at a time $t\geq n$, we may simplify the above expression for $\xi$ as:
%
\begin{multline*}
\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right)
=\frac{1}{n} \times 
\,
\ex \left[ \,\,\, \left|\,\vdead\left(n,\vs\right)\,\right| \, 
\,\colon \,
\text{
$\vs$ is selected randomly from $S_{\Upsilon,\mathcal{K}}$
}
\right]
\\
\Longrightarrow \, 
\Pr \left[ 
\,\left|\,\vdead\left(n,\vs\right)\,\right| \, 
\geq 
n\,\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right)
\,\colon \,
\text{
$\vs$ is selected randomly from $S_{\Upsilon,\mathcal{K}}$
}
\right] > 0 
\end{multline*}
%
As an example, $\xi\left(0.1,G,0.3,0.5,\mathrm{random}\right)=0.9$ means that with positive probability 
$90\%$ nodes of the network $G$ become insolvent with $\gamma=0.3$ and $\Phi=0.5$ 
if we provide an initial shock to a random subset of $10\%$ of nodes of $G$.
{\em Note that lower values of $\xi$ imply higher global stability of a network}.
For simplicity, we may omit the arguments of $\xi$ when they are clear from the context.
%
A pseudo-code for calculating $\xi$ is shown in Fig.~\ref{ps1}. 

\begin{figure*}[t]
{
\begin{center}
\begin{tabular}{l}
\hline
\\
[-0.1in]
\hspace*{0.15in}
$(*$ {\sf initialization of parameters} $*)$
\\
\hspace*{0.15in}
$t\leftarrow 0$ ; $\vdead\left(0,\vs\right)\leftarrow\emptyset$ ; continue$\,=${\sf TRUE} ; 
\\
\hspace*{0.15in}
$\vs\leftarrow$ set of $\mathcal{K}\!\!n$ nodes selected for initial insolvency based on shocking mechanism $\Upsilon$
\\
[0.05in]
\hspace*{0.15in}
{\bf for} every node $v\in V$ {\bf do} 
\\
\hspace*{0.25in} $\din\left(v,0,\vs\right)\leftarrow\din(v)$ 
\\
\hspace*{0.15in} 
{\bf endfor}
\\
[0.05in]
\hspace*{0.15in}
$(*$ {\sf provide an initial shock} $*)$
\\
[0.05in]
\hspace*{0.15in}
{\bf for} every node $u\in V'$ {\bf do} 
\\
\hspace*{0.25in} $c_u\left(0,\vs\right)\leftarrow c_u-\Phi\,e_u$ 
\\
\hspace*{0.15in} 
{\bf endfor}
\\
[0.05in]
\hspace*{0.15in}
$(*$ {\sf loop until no new node fails} $*)$
\\
[0.05in]
\hspace*{0.05in}
$
\left[
\begin{array}{l}
\text{{\bf while} $\Big(\big( \,\text{continue$\,=${\sf TRUE}}\, \big) \bigwedge \big(\,\vdead\left(t,\vs\right)\neq V\,\big)\Big)$ {\bf do}} 
\\
\left[
\begin{array}{l}
\text{{\bf for} every node $u\in V\setminus\vdead\left(t,\vs\right)$ {\bf do}}
\\
\hspace*{0.1in}
c_u\left(t+1,\vs\right)\leftarrow c_u\left(t,\vs\right)
\\
[0.05in]
\left[
\begin{array}{l}
\text{{\bf for} every node $v\in V\setminus\vdead\left(t,\vs\right)$ {\bf do}}
\\
\hspace*{0.15in}
\text{{\bf if} $\Big( \big( \, c_v\left(t,\vs\right)<0 \, \big) \bigwedge \big(\,  (u,v)\in E\,  \big) \Big)$ {\bf then}}
\hspace*{0.15in}
\text{
$(*$ {\sf propagate shock to in-neighbors} $*)$
}
\\
\hspace*{0.5in}
c_u\left(t+1,\vs\right)\leftarrow c_u\left(t+1,\vs\right)-\dfrac{\min\big\{\,\big|\,c_v\left(t,\vs\right)\,\big|\,,\,\,b_v\,\big\}}{\din\left(v,t,\vs\right)}
\\
\text{{\bf endfor}} 
\end{array}
\right.
\\
[0.05in]
\hspace*{0.1in}
\vdead\left(t+1,\vs\right) \leftarrow \vdead\left(t,\vs\right) ; 
\\
[0.05in]
\hspace*{0.15in}
\text{{\bf if} $c_u\left(t,\vs\right)<0$ {\bf then}} 
\hspace*{0.1in}
\vdead\left(t+1,\vs\right)\leftarrow\vdead\left(t+1,\vs\right)\cup \big\{u\big\}
\\
\hspace*{2.0in}
\text{
$(*$ {\sf node $u$ fails if its equity becomes negative} $*)$
}
\\
\text{{\bf endfor}} 
\end{array}
\right.
\\
[0.05in]
\hspace*{0.1in}
t\leftarrow t+1
\\
[0.05in]
\hspace*{0.1in}
\text{{\bf if} $\left(\,\vdead\left(t,\vs\right)=\vdead\left(t-1,\vs\right)\,\right)$ {\bf then}} 
\hspace*{0.1in}
\text{continue$\,\leftarrow\,${\sf FALSE}} 
\\
[0.05in]
\left[
\begin{array}{l}
\text{{\bf for} every node $u\in V\setminus\vdead\left(t,\vs\right)$ {\bf do}}
\\
\hspace*{0.1in}
\din\left(u,t,\vs\right)
=
\Big| \Big\{ v \colon \big( \, (v,u)\in E \, \big)  \wedge \big( \, v\in V\setminus\vdead\left(t,\vs\right) \, \big) \Big\} \Big|
\\
\hspace*{0.5in}
\text{
$(*$ {\sf update in-degrees of alive nodes to exclude freshly dead nodes} $*)$
}
\\
\text{{\bf endfor}} 
\end{array}
\right.
\\
\text{{\bf endwhile}} 
\end{array}
\right.
$
\\
[0.05in]
$\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right)\leftarrow \dfrac{\left|\vdead\left(t,\vs\right)\right|}{n}$
\\
\noalign{\smallskip}
\hline
\end{tabular}
\end{center}
}
%
\caption{Pseudo-code for calculating $\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right)$. 
Comments in the pseudo-code are enclosed by $(*$ and $*)$. 
An implementation of the pseudo-code is available
at \protect\url{www2.cs.uic.edu/~dasgupta/financial-simulator-files}.} 
\label{ps1}
%
\end{figure*}






































\subsection{Rationale for the global stability measure}
\label{rat2}

It is possible to think of other alternate measures of global stability than the one quantified above. 
However, the measure introduced above is {\em in tune} with the ideas that references~\cite{E04,NYYA07,HM11,AW12} 
directly (and, some other references such as~\cite{F03,UW04,MA10} implicitly) 
used to empirically study their networks. Thus, in formalizing our global stability measure, 
we have decided to follow the cue provided by other researchers in the banking industry who have studied various insolvency propagation models.
Measures of similar flavor have also been used by prior researchers in social networks in the context of influence
maximization~\cite{Chen08,CWY09}.

\section{Simulation environment and explored parameter space}
\label{sim-sec}

In Table~\ref{sum-par} we provide a summary of our simulation environment and explored parameter space. Individual 
components of the summary are discussed in Sections~\ref{topo}--\ref{para}.

\subsection{Network topology\protect\footnote{One may obviously ask: {\em why not use ``real'' networks}? There are several obstacles however
that make this desirable goal impossible to achieve. For example: {\bf ({\em a})} Due to their highly sensitive nature, such networks with all relevant parameters
are {\em rarely} publicly available. {\bf ({\em b})} For the kind of inferences that we make in this paper, we need hundreds of thousands of large networks to 
have any statistical validity (in this paper, we explore more than 700,000 networks).}}
\label{topo}

\renewcommand{\tabcolsep}{3pt}
\begin{table*}
\begin{tabular}{l l l c}
\cline{1-3}
\noalign{\smallskip}
parameter & \multicolumn{2}{c}{explored values for the parameter} & 
\\
\cline{1-3}
\noalign{\smallskip}
\multirow{3}{*}{network type} &                 {homogeneous}                    & 
& \multirow{14}{*}{\scalebox{2}[20]{\bf \}} $\!\!\!\!\!\!$ \begin{tabular}{c} total \\ number of \\ parameter \\ combinations \\ $>\,700,000$ \\[1.0in] \\ \end{tabular} } 
{\smallskip}
\\ 
\cline{2-3}
\noalign{\smallskip}
                                     &  \multirow{2}{*}{$(\alpha,\beta)$-heterogeneous} & $\alpha=0.1,\,\,\beta=0.95$ 
& \\ 
                                     &                                                         & $\alpha=0.2,\,\,\beta=0.6$ 
& \\ \cline{1-3}
\noalign{\smallskip}
%
\multirow{5}{*}{network topology} &  \multirow{3}{*}{directed scale-free           } & \hspace*{-0.3in}average degree $1$ (in-arborescence) 
& \\ [-0.00in] 
                                         &                                                         & average degree $3$ 
& \\ [-0.01in]
                                         &                                                         & average degree $6$
& \\ [-0.01in] \cline{2-3}
\noalign{\smallskip}
                                         &  \multirow{2}{*}{directed Erd\"{o}s-R\'{e}nyi}   &  average degree $3$ 
& \\ 
                                         &                                                                    &  average degree $6$ 
& \\ \cline{1-3}
\noalign{\smallskip}
%
\multirow{1}{*}{shocking mechanism           } &  idiosyncratic, coordinated                     &                     
& \\[-0.00in] 
\cline{1-3}
\noalign{\smallskip}
number of nodes                   &  $50,\,100,\,300$                                    &                  
& \\
\cline{1-3}
\noalign{\smallskip}
$\nicefrac{E}{I}$              & \multicolumn{2}{l}{$0.25,0.5,0.75,1,1.25,1.5,1.75,2,2.25,2.5,2.75,3,3.25,3.5$}
& 
\\
\cline{1-3}
\noalign{\smallskip}
$\Phi$                           & $0.5,\,0.6,\,0.7,\,0.8,\,0.9$                             &          
& \\
\cline{1-3}
\noalign{\smallskip}
$\mathcal{K}$                  & \multicolumn{2}{l}{$0.1,\,0.2,\,0.3,\,0.4,\,0.5,\,0.6,\,0.7,\,0.8,\,0.9$}
& \\
\cline{1-3}
\noalign{\smallskip}
$\gamma$                         & $0.05,\,0.1,\,0.15,\dots,\Phi-0.05$                   &               
& \\
\cline{1-3}
\end{tabular}
%
\caption{\label{sum-par}A summary of simulation environment and explored parameter space.}
%
\end{table*}
\renewcommand{\tabcolsep}{6pt}

We consider two topology models previously used by economists to generate random financial networks: 
%
\begin{itemize}
\item
the {\em directed scale-free} ({\sf SF}) network model~\cite{BaAl99} that has been 
used by prior financial network researchers such as~\cite{SR10,M11,ACM11,CMS10}, and 

\item
the {\em directed Erd\"{o}s-R\'{e}nyi} ({\sf ER}) network model~\cite{Bo03} that has been used by prior financial network researchers such as~\cite{A10,GK08,MGS09,CD09,CNSW00}.
\end{itemize}
%

\begin{wrapfigure}[8]{R}{0pt}
%%% in-arborescence
\scalebox{0.55}[0.35]{
\begin{pspicture}(-2.5,-2.2)(7,3.4)
\psset{xunit=0.75cm,yunit=0.75cm}
\rput[mr](-0.9,0){\Huge\bf root}
%%%%%%
\pscircle[origin={0,0},linewidth=2pt](0,0){0.3}
%%%%%%
\pscircle[origin={3,-3},linewidth=2pt](0,0){0.3}
\pscircle[origin={3,0},linewidth=2pt](0,0){0.3}
\pscircle[origin={3,3},linewidth=2pt](0,0){0.3}
%%%%%%
\pscircle[origin={6,-4},linewidth=2pt](0,0){0.3}
\pscircle[origin={6,-3},linewidth=2pt](0,0){0.3}
\pscircle[origin={6,-2},linewidth=2pt](0,0){0.3}
%
\pscircle[origin={6,0},linewidth=2pt](0,0){0.3}
%
\pscircle[origin={6,2},linewidth=2pt](0,0){0.3}
\pscircle[origin={6,4},linewidth=2pt](0,0){0.3}
%%%%%%
\pscircle[origin={9,-4},linewidth=2pt](0,0){0.3}
\pscircle[origin={9,-3},linewidth=2pt](0,0){0.3}
\pscircle[origin={9,-2},linewidth=2pt](0,0){0.3}
%
\pscircle[origin={9,3},linewidth=2pt](0,0){0.3}
\pscircle[origin={9,5},linewidth=2pt](0,0){0.3}
%%%%%%
%%%%%%
%%%%%%
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(2.7,-3)(0,-0.3)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(2.7,0)(0.3,0)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(2.7,3)(0,0.3)
%%%%%%
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(5.7,-3)(3.3,-3)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(5.7,-2)(3,-2.7)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(5.7,-4)(3,-3.3)
%
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(5.7,0)(3.3,0)
%
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(5.7,2)(3,2.7)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(5.7,4)(3,3.3)
%%%%%%
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(8.7,-4)(6.3,-4)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(8.7,-3)(6.1,-3.9)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(8.7,-2)(6,-3.7)
%
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(8.7,3)(6,3.7)
\psline[origin={0,0},linewidth=2pt,linecolor=black,arrowsize=1.5pt 4]{->}(8.7,5)(6,4.3)
%
%%%%%%
\psframe[origin={0,0},linewidth=2pt,linestyle=dashed](-0.75,-4.5)(0.75,5.5)
\rput(0,6.4){\Huge$\pmb{L_1}$}
%
\psframe[origin={3,0},linewidth=2pt,linestyle=dashed](-0.75,-4.5)(0.75,5.5)
\rput(3,6.4){\Huge$\pmb{L_2}$}
%
\psframe[origin={6,0},linewidth=2pt,linestyle=dashed](-0.75,-4.5)(0.75,5.5)
\rput(6,6.4){\Huge$\pmb{L_3}$}
%
\psframe[origin={9,0},linewidth=2pt,linestyle=dashed](-0.75,-4.5)(0.75,5.5)
\rput(9,6.4){\Huge$\pmb{L_4}$}
%
\end{pspicture}
}
%%
\caption{\label{in-arb-fig}An in-arborescence graph.}
\end{wrapfigure}

\noindent
Generation of directed {\sf ER} networks is computationally trivial: given a value $0<p<1$ that parameterizes the {\sf ER} network, for every {\em ordered} pair of distinct nodes $(u,v)$
we let $\Pr\big[(u,v)\in E\big]=\nicefrac{1}{p}$. Letting $p=\nicefrac{d}{n}$ generates a random {\sf ER} network whose average degree is $d$ with high probability.





The directed {\sf SF} networks in this paper are generated using the algorithm outlined by Bollobas \EA~\cite{Bo03}. 
The algorithm works as follows.
Let $a$, $b$, $\eta$, $\delta_{\mathrm{in}}$ (in-degree) and $\delta_{\mathrm{out}}$ (out-degree) 
%
be non-negative real numbers with $a+b+\eta=1$. The initial graph $G(0)$ at step $\ell=0$ has just one node with no edges. 
At step $\ell>0$ the graph $G(\ell)$ has exactly 
$\ell$ edges and a random number $n_{\ell}$ of nodes. For $\ell\geq 0$, $G(\ell+1)$ is obtained from $G(\ell)$ by using the following rules:
%
\begin{itemize}
\item 
With probability $a$, add a new node $v$ together with an edge from $v$ to an existing node $w$, where $w$ is chosen randomly 
such that 
%
\[
\Pr[w=u]=\frac{(d_{\mathrm{in}}(u) + \delta_{\mathrm{in}})}{(\ell + \delta_{\mathrm{in}}\, n_{\ell} )}
\]
%
for every existing node $u$, where $d_{\mathrm{in}}(u)$ is the in-degree of node $u$ in $G(\ell)$. 

\item 
%
With probability $b$, add an edge from an existing node $v$ to an existing node $w$, where $v$ and $w$ are chosen independently, such that 
%
\begin{gather*}
\Pr[v=u]  =  \frac{d_{\mathrm{out}}(u) + \delta_{\mathrm{out}}}{\ell + \delta_{\mathrm{out}} \, n_{\ell} }\,\mbox{ for every existing node $u$}
\\
\Pr[w=u]  =  \frac{d_{\mathrm{in}}(u) + \delta_{\mathrm{in}}}{\ell + \delta_{\mathrm{in}}\,  n_{\ell} }\, \mbox{ for every existing node $u$}
\end{gather*}
%
where $d_{\mathrm{out}}(u)$ is the out-degree of node $u$ in $G(\ell)$. 

\item 
With probability $\eta$, add a new node $w$ and an edge from an existing node $v$ to $w$, where $v$ is chosen such that 
$\Pr[v\!\!\!=\!u]=\dfrac{d_{\mathrm{out}}(u) + \delta_{\mathrm{out}}}{\ell + \delta_{\mathrm{out}}\,  n_{\ell} }$ for every existing node $u$.
\end{itemize}
%
To study the {\em effect of connectivity} on network stability, we generated random {\sf SF} and {\sf ER} networks with average 
degrees\footnote{There are many ways to fix the parameters to get the desired average degree. For example, as observed in~\cite{Bo03}, 
letting $\delta_{\mathrm{out}}=0$ and $\alpha>0$, one obtains 
$
{\mathbb E}\big[\mbox{number of nodes in $G(t)$ of in-degree $x$}\big]\propto x^{-\left(1 + \frac{1+\delta_{\mathrm{in}}(\alpha+\eta)}{\alpha+\beta} \right)}  t \,\,
$
and 
$
{\mathbb E}\big[\mbox{number of nodes in $G(t)$ of out-degree $x$}\big]\propto x^{-\left(\frac{2-\alpha}{1-\alpha}\right)}  t \,\,
$.
 }
of $3$ and $6$.


In addition, to study the effect of sparse hierarchical topology on network stability, 
we used the Bar\'{a}basi-Albert {\em preferential-attachment} model~\cite{BaAl99} to generate random {\em in-arborescence} 
networks. 
In-arborescences are directed rooted trees with all edges oriented towards the root (see Fig.~\ref{in-arb-fig}), and have the following well-known topological properties:
%
\begin{itemize}
\item
They belong to the class of {\em sparsest connected directed acyclic} graphs.

\item
They are {\em hierarchical} networks, \IE, the nodes can be partitioned into levels $L_1,L_2,\dots,L_p$ such that 
$L_1$ has exactly one node (the ``root'') and nodes in any level $L_i$ have directed edges only to nodes in $L_{i-1}$ (see Fig.~\ref{in-arb-fig}). 
The root may model a ``central bank'' that lends to other banks but does not borrow from any bank.
\end{itemize}
%
The algorithm for generating a random in-arborescence network $G$ using the preferential-attachment model~\cite{BaAl99} is as follows:
%
\begin{itemize}
\item  
Initialize $G=(V,E)$ to have one node (the root) and no edges.

\item
Repeat the following steps till $G$ has $n$ nodes: 
%
\begin{itemize}
\item
Randomly select a node $u$ in $G$ such that, for every node $v$ in $G$, 
$
\Pr[u=v]=\frac{\mathrm{deg}(v)}{\sum_{w\in V}\mathrm{deg}(w)}
$
where $\mbox{deg}(y)$ denotes the degree of node $y$ in $G$.

\item
Add a new node $x$ and an undirected edge $\{x,u\}$ in $G$.
\end{itemize}
%

\item
Orient all the edges towards the root.
\end{itemize}
%

\subsection{Shocking mechanisms $\Upsilon$}
\label{shock-def}

Recall that a shocking mechanism $\Upsilon$ provides a rule to select the initial subset of nodes to be shocked.
The following two mechanisms are used to select the nodes to receive the initial shock.

\vspace*{0.1in}
\noindent
{\bf Idiosyncratic (random) shocking mechanism}
%
We select a subset of nodes {\em uniformly at random}. This corresponds to random idiosyncratic initial insolvencies of banks, and 
is a choice that has been used by prior researchers such as~\cite{NYYA07,AW12,HM11,GK08,MA10}.

\vspace*{0.1in}
\noindent
{\bf Coordinated shocking mechanism}\footnote{While correlated shocking mechanisms affecting a correlated subset of banks are relevant in practice,
prior researchers such as~\cite{NYYA07,HM11,AW12,GK08,MA10} have mostly used idiosyncratic shocking mechanisms.
There are at least two reasons for this. Firstly, idiosyncratic shocks are a {\em cleaner} way to study the stability of the topology of the banking network.
Secondly, it is not {\em a priori} clear what kind of correlations in the shocking mechanism would lead to failure of more nodes
than idiosyncratic shocks in a {\em statistically significant way}.
Our coordinated shocking mechanism intuitively corresponds shocks in which banks that are 
``too big to fail'' in terms of their assets are correlated. Our conclusion 
\scalebox{1.5}[1.5]{\ding{177}}
shows that coordinated shocks
do indeed cause more statistically significant damage to the stability of the network as opposed to random shocks.}.
%
In this type of {\em non-idiosyncratic} correlated shocking mechanism, we seek to play an {\em adversarial} 
role\footnote{Usage of adversarial strategies in measuring the worst-case bounds for network properties are very common in the algorithmic literature; 
see, for example, see the book~\cite{BE98}.} in selecting nodes for the initial shock that may cause more damage to the stability of the network. 
The selection of an adversarial strategy depends on whether the network is homogeneous or heterogeneous.
The coordinated shocking mechanism falls under the general category of {\em correlated} shocks where the nodes with 
high (weighted) in-degrees are correlated. 

For homogeneous networks, recall that all nodes have the same share of the total external asset $\E$. However, the total interbank
exposure $b_v$ of a node $v$ is directly proportional to the in-degree of $v$, and, as per
Equation~\eqref{eq1}, nodes with higher inter-bank exposures are 
more likely to transmit the shock to a larger number of {\em other} nodes.
Thus, we play an adversarial role by selecting a set of $\mathcal{K}\,n$ nodes in {\em non-increasing} order of their in-degrees 
starting from a node with the highest in-degree.

For heterogeneous networks, nodes with higher ``weighted'' in-degrees (\IE, with higher values of the sum of {\em weights} of
incoming edges) represent nodes that have larger external assets than other nodes, 
and have more inter-bank exposures. Thus, for heterogeneous networks
we play an adversarial role by selecting $\mathcal{K}\,n$ nodes in non-increasing order of their {\em weighted in-degrees}
starting from a node with the highest weighted in-degree.

\subsection{Network type: $(\alpha,\beta)$-heterogeneous networks}
\label{alphabeta-sec}

Recall that in a heterogeneous network it is possible to have a few banks whose 
external assets or interbank exposures are {\em significantly larger} than the rest of the banks, \IE, it is possible to 
have a few banks that are ``too big'', and thus heterogeneous networks permit investigation of the effect of such big banks on the global stability of the entire
network. To this end, we define a $(\alpha,\beta)$-heterogeneous network as follows.

\begin{definition}[\bf $\,\pmb{(\alpha,\beta)}$-heterogeneous network]\label{defnet}
Let $\widetilde{V}\subseteq V$ be a random subset $V$ of $\alpha n$ nodes and let $\widetilde{E}$ be the set of edges that have at least one end-point from $\widetilde{V}$.
For $0<\alpha,\beta<1$, a $(\alpha,\beta)$-heterogeneous network $G=(V,E)$ is one in which 
the total external and internal assets are distributed in the following manner:
%
\begin{quote}
\begin{description}
\item[\bf Distribution of $\E$:]$\,$
%
\begin{itemize}
\item
distribute $\beta \E$ part of the total external asset $\E$ equally among the $\alpha\,n$ nodes in $\widetilde{V}$, and 

\item
distribute the remaining part $(1-\beta)\E$ of $\E$ equally among the {\em remaining} $(1-\alpha)n$ nodes. 
\end{itemize}
%

\item[\bf Distribution of $\I$:]$\,$
%
\begin{itemize}
\item
Distribute $\beta \I$ part of the total interbank exposure $\I$ equally among a random subset of $\alpha|\widetilde{E}|$
of edges from the edges in $\widetilde{E}$, and 

\item
distribute the remaining part $(1-\beta)\I$ of $\I$ equally among the {\em remaining} $|E|-\alpha|\widetilde{E}|$ edges.
\end{itemize}
%
\end{description}
%
\end{quote}
%
\end{definition}

We performed our simulations for $(\alpha,\beta)$-heterogeneous networks for $(\alpha,\beta)=(0.1,0.95)$ and $(\alpha,\beta)=(0.2,0.6)$.
The combination $(\alpha,\beta)=(0.1,0.95)$ corresponds to the extreme situation in which 95\% of the assets and exposures involve 10\% of banks, thus
creating a minority of banks that are significantly larger than the remaining banks. The other combination $(\alpha,\beta)=(0.2,0.6)$ corresponds to a 
less extreme situation in which there are a larger number of moderately large banks.

\subsection{Other minor details}
\label{para}

To correct statistical biases, for each combinations of parameters, shock types and network types, 
we generated $10$ corresponding random networks and computed the average value of the vulnerability index over these $10$ runs.
For {\sf ER} and {\sf SF} random networks, we selected the values of network generation parameters such that the expected number of edges of the network is 
$3n$ or $6n$ depending on whether we require the average degree of the network to be $3$ or $6$, respectively. 

The minimum difference between two non-identical values of the average vulnerability index over $10$ runs for two $n$-node networks is 
$\nicefrac{1}{(10\,n)}$. Thus, to allow for minor statistical biases introduced by any random graph generation method, we consider 
two vulnerability indices to be same (within the margin of statistical error) if their absolute difference is no more than $\nicefrac{1}{(3\,n)}$, 
which is above $\nicefrac{1}{(10\,n)}$ but no more than 0.7\% of the total range of the vulnerability indices.

Finally, we can assume without loss of generality that $\I=m$, since otherwise if $\mu=\frac{\I}{m}\neq 1$ then we can divide each of the 
quantities $\iota_v$, $b_v$ and $\E$ by $\mu$ without changing the
outcome of the insolvency propagation procedure.

\section{Results}
\label{empiri-sec}

In this section, we discuss our uncovering of many interesting relationships of the stability with other 
relevant parameters of the network based on our comprehensive evaluation and analysis of this stability measure. 
%
It is easy to see that there are many (at least several thousands, but significantly more in most cases) networks in the original sets of networks 
that are compared in two different scenarios in Tables~\ref{table2},\ref{table6},\ref{table8},\ref{table3},\ref{table4and5},\ref{table1},\ref{table10},\ref{table11} and 
related tables in the supplementary documents, thereby assuring the statistical validity of the comparison results.


\subsection{\bf Effect of unequal distribution of total assets $\E$ and $\I$}
\label{jj1}

As our analysis shows, nodes with disproportionately large external assets affect the stability of
the entire network in an {\em adverse} manner, and more uneven distribution of assets among nodes in the network makes the network less stable.

\subsubsection{Effect on global stability}

For the same value of the common parameters $n$, $\frac{\E}{\I}$, $\mathcal{K}$, $\Phi$ and $\gamma$, for the same for network type ({\sf ER}, {\sf SF} or in-arborescence) 
of same average degree (6, 3 or 1) and for the same shocking mechanism $\Upsilon$ (coordinated or idiosyncratic), we compared the value of 
$\xi$ for the homogeneous network with the corresponding values of $\xi$ for $(0.1,0.95)$-heterogeneous and $(0.2,0.6)$-heterogeneous networks.
The comparison results shown in Table~\ref{table2} show most of the entries as being at least 90\%. Thus, we conclude: 

\begin{quote}
{
\scalebox{1.5}[1.5]{\ding{172}}
\em 
networks with all nodes having the same external assets display higher stability 
over similar networks with fewer nodes having disproportionately higher external assets.
}
\end{quote}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Table for xi for homogeneous vs heterogeneous networks
%
\begin{table}[ht]
%
\renewcommand{\tabcolsep}{2pt}
%
\caption{Comparison of stabilities of $(\alpha,\beta)$-heterogeneous networks with their homogeneous counter-parts over all parameter ranges.
The numbers are the percentages of data points for which $\xi_{\mathrm{(\alpha,\beta)-heterogeneous}}$ was at least  $\xi_{\,\mathrm{homogeneous}}$.}
\label{table2}
%
{
\begin{center}
\hspace*{-0.1in}
\begin{tabular}{r c | c | c  | c |c | c |c | c |c | c}
\toprule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% column headings for other than first column
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
& 
       \multicolumn{2}{c|}{In-arborescence} 
       & 
      \multicolumn{2}{c|}{ \begin{tabular}{c} {\sf ER} \\ average degree 3 \end{tabular}} 
      &
      \multicolumn{2}{c|}{\begin{tabular}{c} {\sf ER} \\ average degree 6 \end{tabular}} 
      &
      \multicolumn{2}{c|}{\begin{tabular}{c} {\sf SF} \\ average degree 3 \end{tabular}} 
      &
      \multicolumn{2}{c}{\begin{tabular}{c} {\sf SF} \\ average degree 6 \end{tabular}} 
\\
[0.05in]
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
\\
&
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
\smallskip
\\
\cmidrule{2-11}
%
\begin{tabular}{c}
coordinated \\ shock
\end{tabular}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first column ends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% other columns and data points
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
          & 66.91\% & 60.22\% & \bf 99.26\% & \bf 98.91\% & \bf 98.46\% & \bf 98.00\% & \bf 98.22\% & \bf 91.68\% & \bf 99.13\% & \bf 97.4\%
\\
& & & & & & & & & &
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% other columns and data points end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\\
\begin{tabular}{c}
idiosyncratic \\ shock
\end{tabular}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first column ends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% other columns and data points
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
          & \bf 92.75\% & \bf 81.79\% & \bf 97.76\% & \bf 96.81\% & \bf 98.16\% & \bf 97.61\% & \bf 98.86\% & \bf 94.84\% & \bf 98.83\% & \bf 97.22\%
\\
\bottomrule
\end{tabular}
\end{center}
%
}
%
\end{table}


\noindent
{\bf Formal intuition behind the conclusion in \scalebox{1.5}[1.5]{\ding{172}}}

\vspace*{0.1in}
\noindent
In spite of the highly non-linear nature of Equation~\eqref{eq1}, the following formal intuition may help to explain the conclusion in 
\scalebox{1.5}[1.5]{\ding{172}}.

\begin{lemma}[see Section~\ref{g1proof-sec} of the appendix for a proof]\label{g1}
Fix $\gamma$, $\Phi$, $\E$, $\I$ and the graph $G$.
Consider any node $v\in\vs$ and suppose that $v$ fails due to the initial shock. 
For every edge $(u,v)\in E$, let $\Delta_{\,\mathrm{homo}}(u)$ and $\Delta_{\,\mathrm{hetero}}(u)$ be  
the amount of shock received by node $u$ at time $t=1$ if 
$G$ is homogeneous or heterogeneous, respectively. 
Then, 
%
\[
\ex \left[ \Delta_{\,\mathrm{hetero}}(u)\right] \geq \dfrac{\beta}{\alpha}\,\ex \left[ \Delta_{\,\mathrm{homo}}(u)\right]
=
\begin{array}{rl}
9.5
\,
\ex \left[ \Delta_{\,\mathrm{homo}}(u) \right] 
, & \mbox{ if $(\alpha,\beta)=(0.1,0.95)$}
\\
[0.05in]
3
\,
\ex \left[ \Delta_{\,\mathrm{homo}}(u) \right] 
, & \mbox{ if $(\alpha,\beta)=(0.2,0.6)$}
\end{array}
\]
%
\end{lemma}

Lemma~\ref{g1} implies that $\ex \left[ \Delta_{\,\mathrm{hetero}}(u)\right]$ is much bigger than $\ex\left[ \Delta_{\,\mathrm{homo}}(u)\right]$, 
and thus more nodes are likely to fail beyond $t>0$ leading to a lower stability 
for heterogeneous networks.







































\subsubsection{Effect on residual instability}

For homogeneous networks, if the equity to asset ratio $\gamma$ is close enough to the severity of the shock $\Phi$
then the network almost always tends to be perfectly stable, as one would intuitively expect.  
However, the above property is {\em not} true in general for highly heterogeneous networks in the sense that,
even when $\gamma$ is close to $\Phi$, these networks (irrespective of their topologies and densities) have a {\em minimum} amount of
global instability (which we term as the {\em residual instability})\footnote{For visual illustrations to this phenomena, see {\em supplemental} {\sc Fig}.~\ref{newfig1}--\ref{newfig3}.
For example, in {\em supplemental} {\sc Fig}.~\ref{newfig1}, when $\gamma$ is $45\%$ and $\Phi$ is 
only $5\%$ more than $\gamma$, the vulnerability index $\xi$ is approximately $0$ for {\em all} the $9$ combinations of parameters, but 
in {\em supplemental} {\sc Fig}.~\ref{newfig2}--\ref{newfig3} {\em all} the $18$ networks have a value of $\xi\geq 0.1$ 
even when $\gamma$ is $45\%$ and the severity of the shock is 
only $5\%$ more than $\gamma$.}.

In Table~\ref{table6} and {\em supplemental} Tables~\ref{table7}--\ref{supp4-table7} we tabulated residual instabilities for 
different types of homogeneous and heterogeneous networks under coordinated and idiosyncratic shocks. The numbers in these tables show, for 
each combination of network types, $|V|$, shocking mechanism and values of $\Phi$ and $\gamma$ such that $|\Phi-\gamma|=0.05$, the percentage of 
networks with this combination for which the vulnerability index $\xi$ was less than $0.05$, $0.1$ or $0.2$. As the reader will observe, 
all the numbers for heterogeneous networks are significantly lower than their homogeneous counter-parts. Thus, we conclude: 

\begin{quote}
\scalebox{1.5}[1.5]{\ding{173}}
{\em a heterogeneous network, in contrast to its corresponding homogeneous version, 
has a residual minimum instability even if its equity to asset ratio is very large and close to the severity of the shock}.
\end{quote}

\renewcommand{\tabcolsep}{3pt}
\begin{table}[htbp]
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks. 
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.
{\bf See also {\em supplementary} Tables~\ref{table7}--\ref{supp4-table7}}.}
\label{table6}
%
\begin{center}
\scalebox{0.85}[0.75]
{
%
\begin{tabular}{c c r      r r r | r r r}
\toprule
&
&
&
\multicolumn{6}{c}{\bf coordinated shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.5,\gamma=0.45$}
&
\multicolumn{3}{c}{$\Phi=0.5,\gamma=0.40$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\noalign{\smallskip}
\cline{1-9}
\noalign{\smallskip}
\multirow{15}{*}{\begin{tabular}{c}$|V|$ \\ $=$ \\ $50$ \end{tabular} }
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 73\%  & \bf 73\%  &  \bf 73\% & \bf 0\% \bf & \bf 31\%  & \bf 59\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 89\%  & \bf 100\%  &  \bf 100\% & \bf 43\% \bf & \bf 84\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 44\%  & \bf 84\%  &  \bf 100\% & \bf 25\% \bf & \bf 57\%  & \bf 88\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\noalign{\smallskip}
\cline{2-9}
\noalign{\smallskip}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% \bf & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 0\%  &  1\% & 0\% \bf & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
8\%  & 9\%  &  10\% & 2\% \bf & 6\%  & 6\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
2\%  & 6\%  &  15\% & 0\% \bf & 2\%  & 5\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
18\%  & 23\%  &  30\% & 9\% \bf & 10\%  & 11\%
\\
\noalign{\smallskip}
\cline{2-9}
\noalign{\smallskip}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% \bf & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
4\%  & 7\%  &  19\% & 2\% \bf & 6\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
8\%  & 12\%  &  24\% & 6\% \bf & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
2\%  & 6\%  &  22\% & 0\% \bf & 2\%  & 18\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
8\%  & 12\%  &  24\% & 7\% \bf & 8\%  & 16\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\multirow{15}{*}{ \begin{tabular}{c} $|V|$ \\ $=$ \\ $100$ \end{tabular} }
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 73\%  & \bf 73\%  &  \bf 73\% & \bf 0\% \bf & \bf 34\%  & \bf 73\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 66\%  & \bf 100\%  &  \bf 100\% & \bf 25\% \bf & \bf 64\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 29\%  & \bf 61\%  &  \bf 100\% & \bf 20\% \bf & \bf 42\%  & \bf 83\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 90\% \bf & \bf 100\%  & \bf 100\%
\\
\noalign{\smallskip}
\cline{2-9}
\noalign{\smallskip}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 0\%  &  6\% & 0\% & 0\%  & 1\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
6\%  & 6\%  &  6\% & 4\% & 6\%  & 6\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 0\%  &  7\% & 0\% & 0\%  & 3\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
6\%  & 10\%  &  15\% & 6\% & 6\%  & 6\%
\\
\noalign{\smallskip}
\cline{2-9}
\noalign{\smallskip}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 6\%  &  16\% & 0\% & 4\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
6\%  & 7\%  &  16\% & 6\% & 6\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 2\%  &  14\% & 0\% & 1\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 8\%  &  17\% & 6\% & 7\%  & 16\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\multirow{15}{*}{ \begin{tabular}{c} $|V|$ \\ $=$ \\ $300$ \end{tabular}}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 73\%  & \bf 73\%  &  \bf 73\% & \bf 0\% \bf & \bf 55\%  & \bf 73\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 71\%  & \bf 97\%  &  \bf 100\% & \bf 22\% \bf & \bf 60\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 22\%  & \bf 44\%  &  \bf 86\% & \bf 18\% \bf & \bf 36\%  & \bf 74\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 88\% \bf & \bf 100\%  & \bf 100\%
\\
\noalign{\smallskip}
\cline{2-9}
\noalign{\smallskip}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 0\%  &  6\% & 0\% & 0\%  & 1\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
6\%  & 6\%  &  6\% & 0\% & 6\%  & 6\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 0\%  &  10\% & 0\% & 0\%  & 2\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
6\%  & 6\%  &  16\% & 6\% & 6\%  & 6\%
\\
\noalign{\smallskip}
\cline{2-9}
\noalign{\smallskip}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 6\%  &  16\% & 0\% & 4\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
6\%  & 6\%  &  16\% & 6\% & 6\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 0\%  &  13\% & 0\% & 0\%  & 12\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
6\%  & 7\%  &  16\% & 6\% & 6\%  & 16\%
\\
\bottomrule
\end{tabular}
%
}
\end{center}
%
\end{table}
\renewcommand{\tabcolsep}{6pt}





\subsection{\bf Effect of total external assets}

A controversial belief regarding the cause of the collapse of many major financial institutions around 2007 
asserts that removal of the separation between investment and consumer banking
allowed a ripple effect of insolvencies of individual banks to other banks~\cite{ET08,C09}. 
In our setting, the quantity $\nicefrac{\E}{\I}$ controls the total (normalized) amount of
external investments of all banks in the network. Thus, varying the ratio $\nicefrac{\E}{\I}$ allows us to investigate the role of
the magnitude of total external investments on the stability of our banking network (see Table~\ref{table8}).
%
All the entries in Table~\ref{table8} are close to $0$,
showing that heterogeneous networks exhibited {\em very small} average changes in the vulnerability index $\xi$
when $\nicefrac{E}{I}$ was varied. Thus, we conclude:

\begin{quote}
\scalebox{1.5}[1.5]{\ding{174}}
%
{\em for heterogeneous banking networks, global stabilities are affected very little by the amount of the total external asset $\E$ in the system}.
\end{quote}

\noindent
Visual illustrations of \scalebox{1.5}[1.5]{\ding{174}}
are shown in {\em supplemental} {\sc Fig}. \ref{newfig4} and {\sc Fig}. \ref{newfig5} for homogeneous and heterogeneous networks, respectively.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% table for average change of E for heterogeneous networks
\begin{table}
{%\normalsize
%
\caption{Absolute values of the largest change of the vulnerability index $\xi$ in the range $0.25\leq\nicefrac{\E}{\I}\leq 3.5$.}
\label{table8}
%
\hspace*{-0.0in}
%
\begin{center}
%
\begin{tabular}{r c c}
\toprule
& \multicolumn{2}{c}{\hspace*{-0.3in}average values of $\displaystyle\,\,\Big|\,\max_{0.25\leq \frac{\E}{\I}\leq 3.5} \big\{ \xi \big\} {-} \!\!\! \min_{\,0.25\leq \frac{\E}{\I}\leq 3.5} \big\{ \xi \big\} \,\Big|$}
\\[0.1in]
& coordinated shock & idiosyncratic shock 
\\
\noalign{\smallskip}
\cline{2-3}
\noalign{\smallskip}
$(0.1,0.95)$-heterogeneous in-arborescence & \bf 0.017 & \bf 0.045
\\
[0.02in]
$(0.2,0.6)$-heterogeneous in-arborescence & \bf 0.007 & \bf 0.017
\\
[0.02in]
$(0.1,0.95)$-heterogeneous {\sf ER}, average degree 3 & \bf 0.066 & \bf 0.073 
\\
[0.02in]
$(0.2,0.6)$-heterogeneous {\sf ER}, average degree 3 & \bf 0.040 & \bf 0.041
\\
[0.02in]
$(0.1,0.95)$-heterogeneous {\sf ER}, average degree 6 & \bf 0.111 & \bf 0.116
\\
[0.02in]
$(0.2,0.6)$-heterogeneous {\sf ER}, average degree 6 & \bf 0.084 & \bf 0.078
\\
[0.02in]
$(0.1,0.95)$-heterogeneous {\sf SF}, average degree 3 & \bf 0.119 & \bf 0.094
\\
[0.02in]
$(0.2,0.6)$-heterogeneous {\sf SF}, average degree 3 & \bf 0.034 & \bf 0.032
\\
[0.02in]
$(0.1,0.95)$-heterogeneous {\sf SF}, average degree 6 & \bf 0.200 & \bf 0.179 
\\
[0.02in]
$(0.2,0.6)$-heterogeneous {\sf SF}, average degree 6 & \bf 0.054 & \bf 0.054
\\
\bottomrule
\end{tabular}
%
\end{center}
}
%
\end{table}
%
%%\renewcommand{\tabcolsep}{6pt}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\subsection{\bf Effect of network connectivity}

Although it is clear that connectivity properties of a banking network 
has a crucial effect on its stability, prior researchers have drawn mixed conclusions on this. For example, 
Allen and Gale~\cite{AG2000} concluded that networks with {\em less} connectivity are {\em more} prone to contagion than networks with higher connectivity due to
improved resilience of banking network topologies with higher connectivity via transfer of proportion of the losses in one bank's portfolio to more banks 
through interbank agreements. 
On the other hand, Babus~\cite{A05} observed that, when the network connectivity is higher, liquidity can be redistributed in the system to make the risk of contagion lower, and 
Gai and Kapadia~\cite{GK08} observed that higher connectivity among banks leads to more contagion effect during a crisis.
The mixed conclusions arise because links between banks have conceptually two {\em conflicting} effects on contagion, namely, 
%
\begin{itemize}
\item
more interbank links increases the opportunity for spreading insolvencies to other banks,

\item
but, more interbank links also provide banks with co-insurance against fluctuating liquidity flows.
\end{itemize}
%
As our findings show, these two conflicting effects have different strengths in homogeneous versus highly 
heterogeneous networks, thus justifying the mixed conclusions of past researchers.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Table for xi versus average degree comparison for homogeneous networks
%
\begin{table}[htbp]
%
\caption{Effect of connectivity on the stability for homogeneous networks under 
coordinated and idiosyncratic shocks. The percentage shown for a comparison of the type ``network A versus network B'' indicates
the percentage of data points for which the stability of networks of type A was at least as much as that of networks of type B.}
\label{table3}
%
\begin{center}
%
\begin{tabular}{c | c || c | c}
\toprule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% headings
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\multicolumn{2}{c||}{{\sf ER} average degree 3 versus {\sf ER} average degree 6} 
         & \multicolumn{2}{c}{{\sf SF}  average degree 3 versus {\sf SF} average degree 6} 
\\
[0.03in]
    $\,\,\,\,\,$ coordinated shock & idiosyncratic shock
        & $\,\,\,\,\,$ coordinated shock & idiosyncratic shock
\\
& & & 
\\
\bf 97.43\% & \bf 97.05\% & \bf 98.89\% & \bf 98.29\% 
\\
\bottomrule
\end{tabular}
%
\end{center}
%
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\vspace*{0.1in}
\noindent
{\bf Homogeneous networks}
%
Recall that in a homogeneous network all banks have the same external asset.
Table~\ref{table3} shows sparser homogeneous networks with lower average degrees to be more stable for same values of other parameters.
Thus, we conclude:
%
\begin{quote}
\scalebox{1.5}[1.5]{\ding{175}}
%
{\em for homogeneous networks, higher connectivity leads to lower stability}.
\end{quote}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Table for xi versus average degree comparison for heterogeneous networks
\begin{table}
%
\caption{Effect of connectivity on the stability under coordinated and idiosyncratic shocks 
for {\bf (A)} $(\alpha,\beta)$-heterogeneous {\sf ER} and {\sf SF} networks
and {\bf (B)} $(\alpha,\beta)$-heterogeneous in-arborescence versus $(\alpha,\beta)$-heterogeneous {\sf SF} networks.
The percentage shown for a comparison of the type ``network A versus network B'' indicates
the percentage of data points for which the stability of networks of type A was at least as much as that of networks of type B.}
%
\label{table4and5}
%
\renewcommand{\tabcolsep}{2pt}
%
\begin{center}
\scalebox{0.82}[0.82]
{
%
\begin{tabular}{c c | c c | c c | c c}
%
\toprule
\multicolumn{2}{c|}{(0,1,0.95) {\sf ER} average degree 6}
     & \multicolumn{2}{c|}{(0.2,0.6) {\sf ER} average degree 6}
           & \multicolumn{2}{c|}{(0,1,0.95) {\sf SF} average degree 6}
              & \multicolumn{2}{c}{(0.2,0.6) {\sf SF} average degree 6}
\\
\multicolumn{2}{c|}{versus}
     & \multicolumn{2}{c|}{versus}
           & \multicolumn{2}{c|}{versus}
              & \multicolumn{2}{c}{versus}
\\
\multicolumn{2}{c|}{(0,1,0.95) {\sf ER} average degree 3}
     & \multicolumn{2}{c|}{(0.2,0.6) {\sf ER} average degree 3}
           & \multicolumn{2}{c|}{(0,1,0.95) {\sf SF} average degree 3}
              & \multicolumn{2}{c}{(0.2,0.6) {\sf SF} average degree 3}
\\
\hline
 coordinated & 
    idiosyncratic & 
         coordinated & 
           idiosyncratic & 
                coordinated & 
                   idiosyncratic & 
                        coordinated & 
                           idiosyncratic 
\\
 shock & 
    shock & 
         shock & 
           shock & 
                shock & 
                   shock & 
                       shock & 
                          shock 
\\
& & & & & & & 
\\
 \bf 89.3\% 
   & \bf 82.39\% 
        & \bf 68.12\% 
           & \bf 61.46\% 
           & \bf 85.51\% 
                & \bf 73.81\% 
                 & \bf 69.29\% 
                     & \bf 73.07\% 
\\
\bottomrule
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\\
\multicolumn{8}{c}{\bf\normalsize (A)}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\\
\toprule
\multicolumn{4}{c|}{(0,1,0.95) {\sf SF} average degree 3 and average degree 6} & \multicolumn{4}{c}{(0.2,0.6) {\sf SF} average degree 3 and average degree 6}
\\
\multicolumn{4}{c|}{versus} & \multicolumn{4}{c}{versus}
\\
\multicolumn{4}{c|}{(0.1,0.95)-heterogeneous in-arborescence ({\sf SF} ave. degree 1)}
           & \multicolumn{4}{c}{(0.2,0.6)-heterogeneous in-arborescence ({\sf SF} ave. degree 1)}
\\
\hline
               \multicolumn{2}{c}{coordinated shock} & 
                  \multicolumn{2}{c|}{idiosyncratic shock} & 
                       \multicolumn{2}{c}{coordinated shock} & 
                          \multicolumn{2}{c}{idiosyncratic shock} 
\\
\multicolumn{4}{c|}{} & \multicolumn{4}{c}{}
\\
                    \multicolumn{2}{c}{\bf 85.7\%} 
                       & \multicolumn{2}{c|}{\bf 81.86\%} 
                        & \multicolumn{2}{c}{\bf 56.21\%} 
                           & \multicolumn{2}{c}{\bf 51.07\%} 
\\
\bottomrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\\
\multicolumn{8}{c}{\bf\normalsize (B)}
%
\end{tabular}
}
%
\end{center}
%
\renewcommand{\tabcolsep}{6pt}
\end{table}

\vspace*{0.1in}
\noindent
{\bf Heterogeneous networks}
%
In a heterogeneous network,  
there {\em are} banks that are ``too big'' in the sense that these banks have much larger external assets and inter-bank exposures compared to the remaining banks.
Table~\ref{table4and5} shows that for heterogeneous network models
denser networks with higher average degree are more stable than the corresponding sparser networks for same values of other parameters, 
especially when the heterogeneity of the network is larger (\IE, when $\alpha=0.1,\beta=0.95$).
Thus, we conclude:
%
\begin{quote}
\scalebox{1.5}[1.5]{\ding{176}}
%
{\em for heterogeneous networks, higher connectivity leads to higher stability}.
\end{quote}
%

\vspace*{0.1in}
\noindent
{\bf Formal intuition behind the conclusions in \scalebox{1.5}[1.5]{\ding{175}} and \scalebox{1.5}[1.5]{\ding{176}}}

\vspace*{0.1in}
\noindent
Informally, conclusions 
\scalebox{1.5}[1.5]{\ding{175}} and \scalebox{1.5}[1.5]{\ding{176}}
indicate that 
in homogeneous networks higher connectivity leads to more opportunity for spreading insolvencies to other banks whereas in heterogeneous networks 
higher connectivity provides banks with co-insurance against fluctuating liquidity flows through shared interbank assets. However, a precise 
formal treatment of mechanism that drives such conclusions is complicated due to several reasons such as the random nature of the networks, 
the randomness in asset distribution for heterogeneous networks and the non-linear nature of the insolvency propagation equation. Nevertheless, 
we provide the following, somewhat simplified, formal reasoning.
We will use the following notations and conventions\footnote{In standard algorithmic analysis terminologies, $f\approx g$ implies $\frac{f(r)}{g(r)}=1\pm\mathrm{o}(1)$.}:
%
\begin{itemize}
\item
$\dave=\frac{|E|}{n}$ will denote the average degree of a graph $G$. It is assumed that $\dave$ is a small positive integer constant independent of $n$ (\EG, in our
simulation work, $\dave\in\{1,3,6\}$).

\item
$\Delta x$ will denote a small change for the value $x$ of a variable.

\item
For two functions $f(r)$ and $g(r)$ of a variable $r$, we will use the notation $f\approx g$ (respectively, $f \lessapprox g$, $f \gtrapprox g$) if 
$\lim\limits_{r \to \infty} \frac{f(r)}{g(r)}=1$ 
(respectively, $\lim\limits_{r \to \infty} \frac{f(r)}{g(r)}\leq 1$,  $\lim\limits_{r \to \infty} \frac{f(r)}{g(r)}\geq 1$).

\item
The standard phrase ``with high probability'' (or {\tt w.h.p.} in short) refers to a probability $p(n)$ such that $\lim_{n\to\infty}p(n)=0$. 

\item
If necessary, we will use the superscripts ``homo'' and ``hetero'' to denote the value of a quantity for homogeneous and heterogeneous networks, respectively.
\end{itemize}
%
Consider a node $v\in\vs$ with $\din(v)>1$ and suppose that $v$ fails due to the initial shock at $t=0$. By Equation~\eqref{eq1}, for every edge $(u,v)\in E$, the amount of shock 
$u$ receives from $v$ is given by $\B=\min \big\{\A,\,c_1\big\}$ with 
%
\begin{eqnarray}
\A
&
=
&
\frac
{
\Phi \left( c_1 \, \din(v) - c_1 \, \dout(v) + c_2 \, \E \right) \,-\, \gamma \left( c_1 \, \din(v) + c_2 \, \E \right)
}
{
\din(v)
}
\nonumber
\\
&
=
&
c_1 \big( \Phi - \gamma \big) 
+ 
c_2 \big(\Phi - \gamma \big) \frac{\E}{\din(v)} 
- c_1 \Phi  \frac{\dout(v)}{\din(v)}
\label{eq2}
\end{eqnarray}
%
for some appropriate positive quantities $c_1$ and $c_2$ that may be estimated as follows:
%
\begin{itemize}
\item
If $G$ is homogeneous then $c_1^{\mathrm{homo}}=\frac{\I}{n\,\dave}=1$ and $c_2^{\mathrm{homo}}=\frac{1}{n}$. 

\item
If $G$ is $(\alpha,\beta)$-heterogeneous then $c_1^{\mathrm{hetero}}$ and $c_2^{\mathrm{hetero}}$ are random variables independent of $\dave$.
Using the notations in Definition~\ref{defnet} the expected value of $c_2^{\mathrm{hetero}}$ may be estimated as follows: 
%
\begin{eqnarray*}
\ex\left[c_2^{\mathrm{hetero}}\right] & = & 
\frac{
\Pr\left[v\in\widetilde{V}\right] \frac{\beta\,\E}{\alpha\,n}
+
\Pr\left[v\notin\widetilde{V}\right] 
\frac{(1-\beta)\,\E}{(1-\alpha)\,n}
}{\E}
=
\frac{
\alpha\,\frac{\beta\,\E}{\alpha\,n}
+ (1-\alpha)\, \frac{(1-\beta)\,\E}{(1-\alpha)\,n}
}{\E}
=\frac{1}{n}
\end{eqnarray*}
%
The expected value of $c_1^{\mathrm{hetero}}$ depend on the nature ({\sf SF} or {\sf ER}) of the random network; its estimation is therefore deferred until later.
\end{itemize}
%
Our goal is to provide evidence for a claim of the following nature for either random {\sf SF} or random {\sf ER} networks:

\begin{quote}
\em
For many realistic network parameter combinations, {\tt w.h.p.} increasing connectivity from $d$ to $d+\Delta d$ 
decreases the expected amount of shock 
transmitted by a failed node $v$ to $u$ in homogeneous networks (causing improved stability) 
but increases the expected amount of shock 
transmitted by a failed node $v$ to $u$ in heterogeneous networks (leading to worse stability).
\end{quote}




\paragraph{\bf The case of random {\sf SF} networks}
%
If $G$ is a directed {\sf SF} network, then the discrete probability density function for the degree of any node $v$ in $G$ is given by:
%
\[
\forall \, k\in \{1,2,\dots,n-1\} \colon 
\Pr\big[ \din(v)=k \big] 
=
\Pr\left[ \dout(v)=k \right] 
=
C \, k^{-\mu} 
\]
%
where $\mu>2$ is the constant for the exponent of the distribution and $C>0$ is a constant such that 
$\ex\big[ \din(v)\big] = \ex\left[ \dout(v)\right] = \dave$.
For example, for our random in-arborescence networks, the results in~\cite{BaAl99} imply $\mu=3$.
To simplify exposure, in the following we assume that $\mu=3$, though the analysis can be extended in a straightforward manner
for any other $\mu>2$.
$\zeta(s)=\sum_{x=1}^{\infty}x^{-s}$ is the well-known Riemann zeta function; it is well known that 
$\zeta(s)\approx \sum_{x=1}^{n-1}x^{-s}$ for any $s>2$ and for all large $n$ (see~\cite[page 74-75]{Knuth}) and 
$\zeta(s)<\frac{2^{s-1}}{2^{s-1}-1}$ for any $s>1$ (see~\cite[page 489]{Knuth}).
In particular, it is known that $\zeta(2)=\frac{\pi^2}{6}$, $\zeta(3)=1.2020569\cdots$ and $\zeta(4)=\frac{\pi^4}{90}$.
Note that 
%
\[
\ex\big[ \din(v)\big] = \dave
\,\equiv\,
\sum_{k=1}^{n-1} k \left( C k^{-3} \right) = \dave
\,\Rightarrow\,
C \approx \frac{\dave}{\zeta(2)} = \frac{6\,\dave}{\pi^2}
\]
%


\begin{lemma}[see Section~\ref{bb1proof-sec} of the appendix for a proof]\label{bb1}
$\displaystyle
\ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0\right]
\approx
\frac{\pi^2}{15}\,\dave
$ 
and 
$\displaystyle
\Var\left[\din(v)\right]
\approx
\frac{6\,\dave}{\pi^2} \,\ln n 
$.
\end{lemma}
















We now provide an estimation of $c_1^{\mathrm{hetero}}$ using the notations in Definition~\ref{defnet}.

\begin{lemma}[see Section~\ref{c1het-lemmaproof-sec} of the appendix for a proof]\label{c1het-lemma}
{\rm\tt W.h.p.} 
$\,\,\,1 + \alpha - \beta - \frac{\alpha\,\beta}{2}
\leq 
\ex\left[c_1^{\mathrm{hetero}}\right]  
\leq 
\frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha}$.
\end{lemma}





























Due to the above lemma, we may assume that 
%
\[
\mbox{\tt w.h.p. } 
\begin{array}{rl}
0.156875
\leq
\ex\left[c_1^{\mathrm{hetero}}\right]  
\leq
0.16, 
& 
\mbox{ if $G$ is $(0.1,0.95)$-heterogeneous}
\\
[0.05in]
0.54
\leq
\ex\left[c_1^{\mathrm{hetero}}\right]  
\leq
0.76, 
& 
\mbox{ if $G$ is $(0.2,0.6)$-heterogeneous}
\end{array}
\]
%
We will investigate the sensitivity of the amount of shock $\A$ transmitted from $v$ to $u$ as the average degree $\dave$ is changed 
while keeping all other parameters the same. For notational convenience, the parameters are normalized such that 
$\I=n\,\dave$ at the initial value $d$ of $\dave$. 
As $\dave$ is increased from $d$ to $d+\Delta d$, 
$\I$ is still kept the same.
Thus, 
%
\[
\I\Big|_{\substack{\mathrm{at} \\ \dave=d+\Delta d}}
=
\I\Big|_{\substack{\mathrm{at} \\ \dave=d}}
\,\Rightarrow \,
c_1^{\mathrm{homo}}
\Big|_{\substack{\mathrm{at} \\ \dave=d+\Delta d}}
=\frac{
\I\Big|_{\substack{\mathrm{at} \\ \dave=d+\Delta d}}
}{n\,\left(d + \Delta d \right)}
=
\frac{n\,d}{n\,\left(d + \Delta d \right)}
=
\frac{d}{d + \Delta d}
\]
%
Equation~\eqref{eq2} gives the following for homogeneous and heterogeneous networks:
%
\begin{itemize}
\item
If $G$ is a homogeneous network then
%
\begin{align*}
& 
\ex\left[\A^{\mathrm{homo}}\,\big|\, \dave=d\right]
\\
\displaybreak[0]
\approx
\,\,\,\,\,
& 
\big( \Phi - \gamma \big) 
+ 
\frac{\E\,\big(\Phi - \gamma \big)}{n} \ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0 \right] 
- \Phi \, \ex\left[\dout(v)\right] \, \ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0 \right]
\\
\displaybreak[0]
=
\,\,\,\,\,
& 
\big( \Phi - \gamma \big) 
+ 
\frac{\pi^2\,\E\,\big(\Phi - \gamma \big)}{15\,n} \,d
- \frac{\pi^2\,\Phi}{15}\,d^2
%%%%%%%%%%%%%%%%%%%%%%%%
\\
\displaybreak[0]
& 
\\
\displaybreak[0]
&
\ex\left[\A^{\mathrm{homo}} \,\big|\, \dave=d+\Delta d \right]
\\
\displaybreak[0]
\approx
\,\,\,\,\,
&
\textstyle
\frac{d}{d+\Delta d}\,
\big( \Phi - \gamma \big) 
+ 
\frac{\E\,\big(\Phi - \gamma \big)}{n} \ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0 \right] 
- 
\frac{d}{d+\Delta d}\,
\Phi \, \ex\left[\dout(v)\right] \, \ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0 \right]
\\
\displaybreak[0]
=
\,\,\,\,\,
&
\frac{d}{d+\Delta d}\,
\big( \Phi - \gamma \big) 
+ 
\frac{\pi^2\,\E\,\big(\Phi - \gamma \big)}{15\,n} \,\big( d + \Delta d \big) 
- 
\frac{d}{d+\Delta d}\,
\frac{\pi^2\,\Phi}{15}\,\big( d + \Delta d \big)^2
%%%%%%%%%%%%%%%%%%%%%%%%
\\
\displaybreak[0]
&
\\
&
\Delta \ex\big[\A^{\mathrm{homo}}\big]
\\
\displaybreak[0]
=
\,\,\,\,\,
&
\ex\left[\A^{\mathrm{homo}} \,\big|\, \dave=d+\Delta d \right]
-
\,
\ex\left[\A^{\mathrm{homo}} \,\big|\, \dave=d \right]
\\
\displaybreak[0]
\approx
\,\,\,\,\,
&
-\,\frac{\Delta d}{d+\Delta d}\,
\big( \Phi - \gamma \big) 
+ 
\frac{\pi^2\,\E\,\big(\Phi - \gamma \big)}{15\,n} \,\Delta d
-
\frac{\pi^2\,\Phi}{15}\,d \,\Delta d
\end{align*}
%

\item
If $G$ is a heterogeneous network then 
%
\begin{multline*}
\ex\big[\A^{\mathrm{hetero}}\big]
=
\big( \Phi - \gamma \big) \, 
\ex\left[ c_1^{\mathrm{hetero}} \right]
+ 
\frac{\E\,\big(\Phi - \gamma \big)}{n} \ex\left[\frac{1}{\din(v)}  \, \Big| \, \din(v)>0 \right] 
\\
\displaybreak[0]
- \Phi \,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\, \ex\left[\dout(v)\right] \, \ex\left[\frac{1}{\din(v)}  \, \Big| \, \din(v)>0 \right]
\end{multline*}
%
which provides the following bounds:
%
\begin{align*}
\ex\left[\A^{\mathrm{hetero}} \,\big| \, \dave =d \right]
&
\approx 
\big( \Phi - \gamma \big) \, 
\ex\left[ c_1^{\mathrm{hetero}} \right]
+ 
\frac{\pi^2\,\E\,\big(\Phi - \gamma \big)}{15\,n} \,d
- 
\frac{\pi^2\,\Phi}{15}\,d^2 \,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\\
\displaybreak[0]
& 
\\
\displaybreak[0]
%%%%%%%%%%%%%%%%%%%%%%%%
\ex\left[\A^{\mathrm{hetero}} \,\big| \, \dave =d + \Delta d \right]
&
\approx
\big( \Phi - \gamma \big) \, 
\ex\left[ c_1^{\mathrm{hetero}} \right]
+ 
\frac{\pi^2\,\E\,\big(\Phi - \gamma \big)}{15\,n} \,\big( d+\Delta d \big)
- 
\frac{\pi^2\,\Phi}{15}\,d^2 \,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\\
\displaybreak[0]
& 
\\
\displaybreak[0]
%%%%%%%%%%%%%%%%%%%%%%%%
\Delta \ex\big[\A^{\mathrm{hetero}}\big]
&
=
\ex\left[\A^{\mathrm{hetero}} \,\big| \, \dave =d + \Delta d \right]
-
\,\,
\ex\left[\A^{\mathrm{hetero}} \,\big| \, \dave =d \right]
\\
\displaybreak[0]
&
\approx \,
\frac{\pi^2\,\E\,\big(\Phi - \gamma \big)}{15\,n} \,\Delta d
-
\frac{\pi^2\,\Phi}{15\,}\,d \,\Delta d\,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\end{align*}
%
\end{itemize}
%
Now note that 
%
\begin{multline}
\Delta \ex\big[\A^{\mathrm{homo}}\big]
\lessapprox 0
\,\Rightarrow \, 
\frac{ \Phi - \gamma }{d+\Delta d}\,
+
\frac{\pi^2\,\Phi\,d}{15}
>
\frac{\pi^2\,\E\,\big(\Phi - \gamma \big)}{15\,n}
\\
\equiv\,
\left(
\frac{ 1 }{d+\Delta d}
+
\frac{\pi^2\,d}{15}
-
\frac{\pi^2\,\E}{15\,n}
\right)
\, \Phi
> 
\left(
\frac{ 1 }{d+\Delta d}
-
\frac{\pi^2\,\E}{15\,n}
\right)
\, \gamma
\label{eq3}
\end{multline}
%
\begin{multline}
\Delta \ex\big[\A^{\mathrm{hetero}}\big]
\gtrapprox 0
\,\Rightarrow \, 
\frac{\E\,\big(\Phi - \gamma \big)}{n} 
>
\Phi\,d\,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\equiv\,
\left(
\frac{\E}{n} 
-
d\,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\right)
\, \Phi
>
\left(
\frac{\E}{n} 
\right)
\, \gamma
\\
\Rightarrow \,
\,
\mbox{\tt w.h.p. }
\,
\left(
\frac{\E}{n} 
-
d\,
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\right)
\, \Phi
>
\left(
\frac{\E}{n} 
\right)
\, \gamma
\label{eq4}
\end{multline}
%
It is easy to verify that constraints~\eqref{eq3}~and~\eqref{eq4} are satisfied for many natural combinations of parameters.
%
In fact, the constraints~\eqref{eq3}~and~\eqref{eq4} are almost always satisfied when $\E$ grows moderately linearly with $n$.
%
To see this informally, note that since $\alpha\ll\beta$ and $\alpha$ is small, 
$\dfrac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha}\approx 1-\beta$ and thus \eqref{eq4} is approximately 
%
\begin{gather}
\left(
\frac{\E}{n} 
-
d\,
\left( 1 - \beta \right)
\,
\right)
\, \Phi
>
\left(
\frac{\E}{n} 
\right)
\, \gamma
\tag*{$(\ref{eq4}')$}
\label{eq4p}
\end{gather}
%
Now suppose that $\E<d(1-\beta)n$. Then, \eqref{eq3} and \eqref{eq4p} are always satisfied since $\Phi>\gamma$.
%
For a numerical example, suppose that $G$ is a $(0.1,0.95)$-heterogeneous network (\IE, $\alpha=0.1$ and $\beta=0.95$), $d=3$, $\Delta d=1$, $\gamma=0.2$ and $\Phi=0.4$. Then 
constraints~\eqref{eq3}~and~\eqref{eq4} reduce to:
%
\[
0.5+0.4\pi^2-\dfrac{2\,\pi^2\,\E}{15\,n} 
>
0.25-\dfrac{\pi^2\,\E}{15\,n} 
\,\,\,\,\,
\,\,\,\,\,
\text{ and }
\,\,\,\,\,
\,\,\,\,\,
\dfrac{2\,\E}{n}-0.94125
>
\dfrac{\E}{n} 
\]
%
and these constraints can be satisfied when $\E$ grows moderately linearly with $n$, \IE, when 
$0.94125\,n<\E<6.38\,n$.









\paragraph{\bf The case of random {\sf ER} networks}
%
In a random {\sf ER} network, the probability of having a particular edge is given by 
the following set of independent Bernoulli trials:
%
\[
\forall \, u, v\in V \text{ with $u\neq v$ } \colon 
\Pr \left[ (u,v) \in E \right] = p =\frac{\dave}{n-1}
\]
%
Thus, for every $k\in \{0,1,2,\dots,n-1\}$: 
%
\begin{align*}
\Pr\big[ \din(v)=k \big] & =\Pr\left[ \dout(v)=k \right]=\binom{n-1}{k} p^k (1-p)^{(n-1)-k}
\\
\displaybreak[0]
\ex\big[\din\big] & =\ex\left[\dout\right]=p\,(n-1)=\dave
\\
\displaybreak[0]
\Var\big[\din(v)\big] & = \Var\left[\dout(v)\right]=p \, (1-p)\,(n-1)=\left(1-\frac{\dave}{n-1} \right)\,\dave
\end{align*}
%
Since $\dave=p\,(n-1)$ is a constant, one can approximate the above binomial distribution by a Poisson's distribution~\cite[page 72]{rozanov} to obtain 
%
\[
\Pr\big[ \din(v)=k \big]=\Pr\left[ \dout(v)=k \right] \approx \e^{-\dave} \, \frac{(\dave)^k}{k!}
\]
%

\begin{lemma}[see Section~\ref{bb3proof-sec} of the appendix for a proof]
\label{bb3}
$%%\displaystyle
\left| \,
\ex\left[\frac{1}{\din(v)}\right]
-
\sum\limits_{k=1}^{\lfloor 3\,\dave + 10 \rfloor } \!\!\!\!\! \!\!\!\!\! \!\!\!\!\! \left(\nicefrac{1}{k}\right) \, \e^{-\dave} \, \frac{(\dave)^k}{k!}
\, \right| 
\lessapprox 10^{-10}
$ 
and 
%%\\
$
\frac{\partial
}{\partial\, d}
\ex\left[\frac{1}{\din(v)} \, \big| \, \dave=d\right]
\approx
\frac{1-\e^{-d}}{d}
$.
\end{lemma}

















For notational convenience, let $\Upsilon(x)=\!\!\!\!\sum\limits_{k=1}^{\lfloor 3x + 10 \rfloor} \frac{1}{k} \, \e^{-x} \, \frac{x^k}{k!}$.
Since $10^{-10}$ is an extremely small number for our purposes, we will just use 
$\ex\left[\frac{1}{\din(v)}\right] \approx \Upsilon\left(\dave\right)$ in the sequel. 
Values of $\Upsilon(x)$ and 
$
\frac{\partial \, \Upsilon(x)}{\partial \, x}=\frac{1-\e^{-x}}{x}
$
for a few small integral values of $x$ are shown in Table~\ref{upsi-table}.
It is easy to see that 
$\lim\limits_{x\to\infty}\Upsilon(x)=0$ and, for large $x$, 
$
\frac{\partial \, \Upsilon(x)}{\partial \, x}\approx \nicefrac{1}{x}
$.

\begin{table*}
%%
\caption{Values of $\Upsilon(x)$ and $\frac{\partial \, \Upsilon(x)}{\partial \, x}$ for a few small integral values of $x$ using straightforward calculations.}
\label{upsi-table}
%%
\begin{center}
\begin{tabular}{c | c c c c c c c c c c c }
\toprule
    & \multicolumn{11}{c}{$x=$} 
\\
    & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 
\\
\cmidrule{2-12}
%
$\Upsilon(x)\approx$ & 0.499 & 0.411 & 0.324 & 0.256 & 0.207 & 0.172 & 0.147 & 0.128 & 0.113 & 0.101 & 0.091
\\
\midrule
$\frac{\partial \, \Upsilon(x)}{x} \approx$ & 0.432 & 0.284 & 0.245 & 0.256 & 0.199 & 0.166 & 0.143 & 0.125 & 0.111 & 0.100 & 0.090
\\
\bottomrule
\end{tabular}
\end{center}
%%%
\end{table*}


As before, we first provide an estimation of $c_1^{\mathrm{hetero}}$ using the notations in Definition~\ref{defnet}.

\begin{lemma}[see Section~\ref{bb4proof-sec} of the appendix for a proof]\label{bb4}
{\rm\tt W.h.p.} 
$\,\,\,
1 + \alpha - \beta - \dfrac{\alpha\,\beta}{2}
\leq 
\ex\left[c_1^{\mathrm{hetero}}\right]  
\leq 
\dfrac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha}
$.
\end{lemma}































Using the above result, the following bounds hold:
%
\begin{itemize}
%%%%%%
%%%%%%
%%%%%%
\item
If $G$ is a homogeneous network then
%
\[
\dfrac{\partial}{\partial \, d}
c_1^{\mathrm{homo}}
\Big|_{\substack{\mathrm{at} \\ \dave=d}}
%%%
=
\lim\limits_{\Delta d \to 0}
\dfrac{
\dfrac{ \I\Big|_{\substack{\mathrm{at} \\ \dave=d+\Delta d}} }{n\,\left(d + \Delta d \right)}
\,-\,
\dfrac{ \I\Big|_{\substack{\mathrm{at} \\ \dave=d}} }{n\,d }
}
{ \Delta d}
=
\lim\limits_{\Delta d \to 0}
\dfrac{
\dfrac{n\,d}{n\,\left(d + \Delta d \right)}
\,-\,
1
}
{ \Delta d}
=
\,-\,
\dfrac{1}{d}
\]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{align*}
&
\ex\left[\A^{\mathrm{homo}} \,\big| \, \dave=d \right]
\\
\displaybreak[0]
=\,\,
&
c_1^{\mathrm{homo}} \,
\big( \Phi - \gamma \big) 
+ 
\frac{\E\,\big(\Phi - \gamma \big)}{n} \ex\left[\frac{1}{\din(v)}  \, \Big| \, \din(v)>0 \right] 
- 
c_1^{\mathrm{homo}} \,
\Phi \, \ex\left[\dout(v)\right] \, \ex\left[\frac{1}{\din(v)}  \, \Big| \, \din(v)>0 \right]
\\
\displaybreak[0]
\approx\,\,
&
c_1^{\mathrm{homo}} \,
\big( \Phi - \gamma \big) 
+ 
\frac{\E\,\big(\Phi - \gamma \big)}{n} \,\Upsilon(d)
- 
c_1^{\mathrm{homo}} \,
\Phi\,d\,\Upsilon(d)
\\
\displaybreak[0]
&
\\
\displaybreak[0]
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&
\frac{\partial}{\partial \, d} \ex\left[\A^{\mathrm{homo}} \,\big| \, \dave=d \right]
\\
\displaybreak[0]
\approx \,\, 
&
\big( \Phi - \gamma \big) 
\,
\frac{\partial}{\partial \, d} 
c_1^{\mathrm{homo}}
\Big|_{\substack{\mathrm{at} \\ \dave=d}}
+
\dfrac{\E\,\big(\Phi - \gamma \big)}{n} \,\frac{\partial}{\partial \, d}\Upsilon(d)
-
\Phi\,
\dfrac{\partial}{\partial \, d} 
\left(
c_1^{\mathrm{homo}}
\Big|_{\substack{\mathrm{at} \\ \dave=d}} \,
d\,\Upsilon(d)
\right)
\\
\displaybreak[0]
= \,\,
&
- \, \dfrac{\Phi - \gamma}{d} \,
+
\left(\dfrac{\E\,\big(\Phi - \gamma \big)}{n}\right) \,\left( \dfrac{1 - \e^{-d}}{d} \right)
-
\Phi \, 
\left(
- \, \Upsilon(d)
+ \, \Upsilon(d)
+ 1 - \e^{-d} 
\right)
\,\,\,\,\,\,\,
\mbox{\begin{tabular}{l} using product rule \\ of derivatives \end{tabular}}
\\
\displaybreak[0]
= \,\,
&
- \, \frac{\Phi - \gamma}{d} \,
+
\left(\frac{\E\,\big(\Phi - \gamma \big)}{n}\right) \,\left( \frac{1 - \e^{-d}}{d} \right)
-
\Phi \, 
\left(
1 - \e^{-d} 
\right)
\end{align*}
%%%%%%%%%%%%%%%%%%%%%%%%











\item
If $G$ is a heterogeneous network then 
%
\begin{multline*}
\ex\big[\A^{\mathrm{hetero}}\big]
=
\big( \Phi - \gamma \big) \, 
\ex\left[ c_1^{\mathrm{hetero}} \right]
+ 
\frac{\E\,\big(\Phi - \gamma \big)}{n} \ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0 \right] 
\\
\displaybreak[0]
- \Phi \,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\, \ex\left[\dout(v)\right] \, \ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0 \right]
\end{multline*}
%
which provides the following bounds {\tt w.h.p.}:
%
\[
\ex\left[\A^{\mathrm{hetero}} \,\big| \, \dave=d \right]
\approx 
\big( \Phi - \gamma \big) \, 
\ex\left[ c_1^{\mathrm{hetero}} \right]
+ 
\frac{\E\,\big(\Phi - \gamma \big)}{n} \,\Upsilon(d)
- 
\Phi\, d \, \Upsilon(d) \,
\ex\left[ c_1^{\mathrm{hetero}} \right]
\]
%%%%%%%%%%%%%%%%%%%%%%%%
\begin{align*}
&
\frac{\partial}{\partial \, d} 
\ex\left[\A^{\mathrm{hetero}} \,\big| \, \dave=d \right]
\\
\displaybreak[0]
\gtrapprox
\,\,
&
\frac{\E\,\big(\Phi - \gamma \big)}{n} \,
\frac{\partial}{\partial \, d} 
\Upsilon(d)
-
\Phi\, \left( \frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha} \right) \, 
\frac{\partial}{\partial \, d} 
\big( \, d \, \Upsilon(d) \, \big)
\\
\displaybreak[0]
=
\,\,
&
\left( \frac{\E\,\big(\Phi - \gamma \big)}{n} \right) \,
\left( \frac{1-\e^{-d}}{d} \right) 
-
\Phi\, \left( \frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha} \right) \, 
\left(
1 - \e^{-d} + \Upsilon(d)
\right)
\,\,\,\,\,\,\,
\mbox{\begin{tabular}{l} using product \\ rule of \\ derivatives \end{tabular}}
\end{align*}
%%%%%%%%%%%%%%%%%%%%%%%%
%
\end{itemize}
%
%
%
%
%
%
%
%
%
%
Now note the following:
%
\begin{multline}
\frac{\partial}{\partial \, d} \ex\left[\A^{\mathrm{homo}} \,\big| \, \dave=d \right]
\lessapprox 0
\\
\displaybreak[0]
\Rightarrow \, 
\frac{\Phi - \gamma}{d} \,
+
\Phi \, 
\left(
1 - \e^{-d} 
\right)
>
\left(\frac{\E\,\big(\Phi - \gamma \big)}{n}\right) \,\left( \frac{1 - \e^{-d}}{d} \right)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\\
\displaybreak[0]
\equiv\,
\left(
\frac{1}{d}
+
1 - \e^{-d}
-
\frac{\E}{n} \,
\left( \frac{1 - \e^{-d}}{d} \right) \,
\right)
\, \Phi
> 
\left(
\frac{ 1}{d}
-
\frac{\E}{n} \,
\left( \frac{1 - \e^{-d}}{d} \right) \,
\right)
\, \gamma
\label{eq5}
\end{multline}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{multline}
\frac{\partial}{\partial \, d} \ex\left[\A^{\mathrm{hetero}} \,\big| \, \dave=d \right]
\gtrapprox 0
\\
\displaybreak[0]
\Rightarrow \, 
\left( \frac{\E\,\big(\Phi - \gamma \big)}{n} \right) \,
\left( \frac{1-\e^{-d}}{d} \right) 
>
\Phi\, \left( \frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha} \right) \, 
\left(
1 - \e^{-d} + \Upsilon(d)
\right)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
\\
\displaybreak[0]
\textstyle
\equiv\,
\left(
\frac{\E }{n}
\left( \frac{1-\e^{-d}}{d} \right) 
-
\left( \frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha} \right) \, 
\left(
1 - \e^{-d} + \Upsilon(d)
\right)
\,
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
\right)
\, \Phi
>
\frac{\E }{n}
\left( \frac{1-\e^{-d}}{d} \right) 
\, \gamma
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\label{eq6}
\end{multline}
%
It is easy to verify that constraints~\eqref{eq5}~and~\eqref{eq6} are satisfied for many natural combinations of parameters.
%
For example, the constraints~\eqref{eq5}~and~\eqref{eq6} are almost always satisfied if $d$ is sufficiently large.
To see this informally, note that if $d$ is large then 
$\frac{1}{d},\e^{-d},\Upsilon(d)\approx 0$.
Moreover, since $\alpha\ll\beta$ and $\alpha$ is small, 
$\frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha}\approx 1-\beta$
and then constraints~\eqref{eq5}~and~\eqref{eq6} reduce to 
%
\begin{gather}
\left(
1 
-
\frac{\E}{n\,d} \,
\right)
\, \Phi
\,
\gtrapprox 
\,
-\,
\frac{\E}{n\,d}
\, \gamma
\,\equiv\,
%%%%%%%%%%%
\Phi
\,
\lessapprox 
\,
\frac{
\frac{\E}{n\,d}
}
{
\frac{\E}{n\,d} \,
-1
}
\, \gamma
\tag*{(\ref{eq5})$^{d\gg 0}$}
\label{eq7}
\end{gather}
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
\begin{gather}
\left(
\,
\frac{\E }{n\,d}
\,
-
\,
1+\beta\,
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
\right)
\, \Phi
\,
\gtrapprox 
\,
\frac{\E }{n\,d}
\, \gamma
\,\equiv\,
\, \Phi
\,
\gtrapprox 
\,
\frac{
\frac{\E }{n\,d}
}
{
\frac{\E }{n\,d}
\,
-
\,
1+\beta\,
}
\,\gamma
\tag*{(\ref{eq6})$^{d\gg 0}$}
\label{eq8}
\end{gather}
%
If $\E>n\,d$ then 
$\frac{ \frac{\E}{n\,d} } { \frac{\E}{n\,d} -1 }>1$ and 
$\frac{ \frac{\E }{n\,d} } { \frac{\E }{n\,d} - 1+\beta} < \frac{ \frac{\E}{n\,d} } { \frac{\E}{n\,d} -1 }$; 
thus both \ref{eq7} and \ref{eq8} can be satisfied by choosing $\Phi$ appropriately with respect to $\gamma$.
%
For a numerical example, suppose that $G$ is a $(0.1,0.95)$-heterogeneous network (\IE, $\alpha=0.1$ and $\beta=0.95$), $d=10$, and $\E=12\,n$. Then 
constraints~\eqref{eq5},\eqref{eq6} reduce to:
%
\[
1.17 < \frac{\Phi}{\gamma} < 11
\]
%
which corresponds to most settings of $\Phi$ and $\gamma$ used in our simulation.







































































%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Table for random vs coordinated shocks
\renewcommand{\tabcolsep}{4pt}
\begin{table}
%
\caption{Comparisons of strengths of coordinated versus idiosyncratic shocks.
The percentages indicate the percentage of total number of data points (combinations of parameters $\Phi$, $\gamma$, $\E$ and $\mathcal{K}$) 
for that network type that resulted in $\xi_c\geq\xi_r$, where $\xi_c$ and $\xi_r$ are the vulnerability indices under coordinated and idiosyncratic shocks, respectively.}
\label{table1}
%
%
\begin{center}
{\small
%
\begin{tabular}{c c  | c  c | c c | c c | c c}
\toprule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% column headings for other than first column
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\multicolumn{10}{c}{$(\alpha,\beta)$-heterogeneous networks}
\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
      \multicolumn{2}{c|}{\footnotesize In-arborescence} 
      &
      \multicolumn{2}{c|}{\footnotesize {\sf ER} average degree 3} 
      &
      \multicolumn{2}{c|}{\footnotesize {\sf ER} average degree 6} 
      &
      \multicolumn{2}{c|}{\footnotesize {\sf SF} average degree 3} 
      &
      \multicolumn{2}{c}{\footnotesize {\sf SF} average degree 6} 
\\
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
&
$\alpha=0.1$ 
&
$\alpha=0.2$ 
\\
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
&
$\beta=0.95$
&
$\beta=0.6$
\\
 & & & & & & & & & 
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% column headings for other than first column end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% other columns and data points
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
                      \bf 56.64\% &             \bf 57.27\% &             \bf 89.66\% &             \bf 90.97\% &             \bf 98.99\% 
                     &             \bf 98.04\% &             \bf 93.16\% &             \bf 64.13\% &             \bf 94.44\% &             \bf 66.48\%
\\
\bottomrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% other columns and data points end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\\
\toprule
%
\multicolumn{10}{c}{homogeneous networks}
\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
%
\multicolumn{2}{c|}{              In-arborescence} 
&
      \multicolumn{2}{c|}{              {\sf ER} average degree 3 } 
      &
      \multicolumn{2}{c|}{              {\sf ER} average degree 6 } 
      &
      \multicolumn{2}{c|}{              {\sf SF} average degree 3 } 
      &
      \multicolumn{2}{c}{              {\sf SF} average degree 6 } 
\\
 & & & & & & & & & 
\\
      \multicolumn{2}{c|}{            \bf 84.62\%} 
      & 
      \multicolumn{2}{c|}{            \bf 74.97\%} 
      &
      \multicolumn{2}{c|}{            \bf 78.59\%} 
      &
      \multicolumn{2}{c|}{            \bf 81.15\%} 
      &
      \multicolumn{2}{c}{            \bf 54.80\%} 
\\
\bottomrule
\end{tabular}
}
\end{center}
%
\end{table}
\renewcommand{\tabcolsep}{6pt}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{\bf Random versus correlated initial failures}
\label{jjj1}

For most parameter combinations, our results, tabulated in Table~\ref{table1}, show that coordinated shocks, which are a type of correlated shocks, resulted in insolvencies of higher
number of nodes as opposed to idiosyncratic shocks for the same network with the same parameters, {\em often by a factor of two or more}.
For example, Table~\ref{table1} shows that for $(0.1,0.95)$-heterogeneous {\sf ER} networks of average degree $6$ 
the vulnerability index under coordinated shocks is at least as much as the vulnerability index under idiosyncratic shocks 
$98.99\%$ of the time.
Thus, we conclude:
%
\begin{quote}
\scalebox{1.5}[1.5]{\ding{177}}
% 
{\em correlated shocking mechanisms are more appropriate to measure the worst-case stability compared to idiosyncratic shocking mechanisms}.
\end{quote}
%
For visual illustrations of \scalebox{1.5}[1.5]{\ding{177}}, see {\em supplemental} {\sc Fig}.~\ref{newfig1-full}---\ref{supp-newfig5-full}.

\subsection{\bf Phase transition properties of stability}
\label{kk2}

Phase transitions are quite common when one studies various topological properties of graphs~\cite{bolo}.
The stability measure exhibits several sharp {\em phase transitions} for various banking networks and combinations of parameters; 
see {\em supplemental} {\sc Fig}.~\ref{newfig1}---\ref{newfig4} for 
visual illustrations.
%%
We discuss two such interesting phase transitions in the following, with  
an intuitive theoretical explanation for one of them.

\subsubsection{Dense homogeneous networks}

Based on the behavior of $\xi$ with respect to $\left(\Phi-\gamma\right)$,  
we observe that, for smaller value of $\mathcal{K}$ and for denser {\sf ER} and {\sf SF} networks under either coordinated or idiosyncratic shocks,  
there is often a {\em sharp} decrease of stability when $\gamma$ was decreased beyond a particular threshold value.
For example, with $\Phi=0.5$ and $\mathcal{K}=0.1$, $100$-node dense (average degree $6$) {\sf SF} and {\sf ER} homogeneous networks exhibited more than ninefold increase in 
$\xi$ around $\gamma=0.15$ and $\gamma=0.1$, respectively; see {\em supplemental} {\sc Fig}.~\ref{newfig1} for visual illustrations.

To investigate the global extent of such a sharp decrease at a threshold value of $\gamma$ in the range $\big[0.05,0.2\big]$, we 
computed, for each of the five homogeneous network types under coordinated shocks and for each values of the parameters $|V|$, $\Phi$, $\frac{\E}{\I}$ and $\mathcal{K}$, , the ratio 
%
\[
\Lambda \left( n, \Phi, \frac{\E}{\I}, \mathcal{K} \right)
=
\dfrac
{
\displaystyle
\max_{0.05\leq\gamma\leq 0.2} \big\{ \xi \big\}- \min_{0.05\leq\gamma\leq 0.2} \big\{ \xi \big\}
}
{
\displaystyle
\max_{\text{entire range of } \gamma} \big\{ \xi \big\}- \min_{\text{entire range of } \gamma} \big\{ \xi \big\}
}
\]
%
that provides the {\em maximum} percentage of the total change of the vulnerability index that occurred within this narrow range of $\gamma$. 
The values of $\Lambda\left( n, \Phi, \frac{\E}{\I}, \mathcal{K} \right)$ for the dense {\sf ER} and {\sf SF} homogeneous networks under coordinated shocks are shown in 
Table~\ref{table10} for
$\Phi=0.5,0.8$ and $\mathcal{K}=0.1,0.2,0.3,0.4,0.5$ (the behaviour of $\xi$ is similar for other intermediate values of $\Phi$).
If the growth of $\xi$ with respect to $\gamma$ was uniform or near uniform over the entire range of $\gamma$, $\Lambda$ would be approximately 
$\lambda=\frac{0.2-0.05}{0.45-0.05}=0.375$; thus, any value of $\Lambda$ significantly higher than $\lambda$ indicates a sharp transition 
within the above-mentioned range of values of $\gamma$. As Table~\ref{table10} shows, 
a {\em significant majority} of the entries for $\Phi\leq 0.8$ and $\kappa\leq 0.2$ are $2\,\lambda$ or more. 













%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% table for sharp increase of xi at gamma=0.1 for homogeneous dense ER and SF networks
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\renewcommand{\tabcolsep}{4pt}
%
\begin{table}[htbp]
%
\caption[]{Values of 
$
\displaystyle
\Lambda \left( n, \Phi, E/I, \mathcal{K} \right)
=
\dfrac
{
\displaystyle
\max_{0.05\leq\gamma\leq 0.2} \big\{ \xi \big\}- \min_{0.05\leq\gamma\leq 0.2} \big\{ \xi \big\}
}
{
\displaystyle
\max_{\text{entire range of } \gamma} \big\{ \xi \big\}- \min_{\text{entire range of } \gamma} \big\{ \xi \big\}
}
$
for homogeneous dense {\sf ER} and {\sf SF} networks under coordinated shocks. Entries that are at least $2\times 0.375$ are shown
in {\bf boldface}.
}
%
\label{table10}
%%%%
\begin{center}
\scalebox{0.8}[0.8]
{%%\footnotesize
%
\begin{tabular}{l l |   lllll    lllll ||   lllll    lllll }
%%%\vspace*{-1in}
\toprule
%%
\multicolumn{12}{c||}{\large \hspace*{0.6in} $\pmb{\Phi=0.5}$}
 & \multicolumn{8}{c}{\large \hspace*{0.6in} $\pmb{\Phi=0.8}$} & & 
\\
 & & \multicolumn{5}{c|}{\normalsize {\sf ER} average degree $6$} & \multicolumn{5}{c||}{\normalsize {\sf SF} average degree $6$}
    & \multicolumn{5}{c|}{\normalsize {\sf ER} average degree $6$} & \multicolumn{5}{c}{\normalsize {\sf SF} average degree $6$}
\\
[0.05in]
 & & \multicolumn{5}{c|}{\normalsize $\pmb{\mathcal{K}=}$} & \multicolumn{5}{c||}{\normalsize $\pmb{\mathcal{K}=}$} 
    & \multicolumn{5}{c|}{\normalsize $\pmb{\mathcal{K}=}$} & \multicolumn{5}{c}{\normalsize $\pmb{\mathcal{K}=}$} 
\\
 $\nicefrac{E}{I}$ & \normalsize \hspace*{-0.1in}$|V|$ 
      & \scalebox{0.7}{0.1} & \scalebox{0.7}{0.2} & \scalebox{0.7}{0.3} & \scalebox{0.7}{0.4} & \multicolumn{1}{l|}{\scalebox{0.7}{0.5}}
        & \scalebox{0.7}{0.1} & \scalebox{0.7}{0.2} & \scalebox{0.7}{0.3} & \scalebox{0.7}{0.4} & \multicolumn{1}{l||}{\scalebox{0.7}{0.5}}
          & \scalebox{0.7}{0.1} & \scalebox{0.7}{0.2} & \scalebox{0.7}{0.3} & \scalebox{0.7}{0.4} & \multicolumn{1}{l|}{\scalebox{0.7}{0.5}}
            & \scalebox{0.7}{0.1} & \scalebox{0.7}{0.2} & \scalebox{0.7}{0.3} & \scalebox{0.7}{0.4} & \multicolumn{1}{l}{\scalebox{0.7}{0.5}}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$0.25$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \bf \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.79}
                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.98}
                                                  & \scalebox{0.9}[0.75]{\bf 0.97}
                                                    & \scalebox{0.9}[0.75]{\bf 0.95}
                                                      & \scalebox{0.9}[0.75]{\bf 0.93}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.74}
                                                                        & \scalebox{0.7}{0.7}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.9}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.85}
                                                                                       & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                                         & \scalebox{0.7}{0.72}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.79}
                              & \scalebox{0.9}[0.75]{\bf 0.81}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.97}
                                                  & \scalebox{0.9}[0.75]{\bf 0.95}
                                                    & \scalebox{0.9}[0.75]{\bf 0.92}
                                                      & \scalebox{0.9}[0.75]{\bf 0.9}
                                                                & \scalebox{0.9}[0.75]{\bf 0.84}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                      & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                        & \scalebox{0.7}{0.72}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.86}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                                       & \scalebox{0.7}{0.71}
                                                                                         & \scalebox{0.7}{0.66}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.93}
                            & \scalebox{0.9}[0.75]{\bf 0.89}
                              & \scalebox{0.9}[0.75]{\bf 0.86}
                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.96}
                                                  & \scalebox{0.9}[0.75]{\bf 0.93}
                                                    & \scalebox{0.9}[0.75]{\bf 0.9}
                                                      & \scalebox{0.9}[0.75]{\bf 0.88}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                      & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                        & \scalebox{0.7}{0.71}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                                     & \scalebox{0.7}{0.71}
                                                                                       & \scalebox{0.7}{0.63}
                                                                                         & \scalebox{0.7}{0.59}
\\
\hline
\multirow{3}{*}{\scalebox{0.75}{$0.5$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.79}
                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.98}
                                                  & \scalebox{0.9}[0.75]{\bf 0.97}
                                                    & \scalebox{0.9}[0.75]{\bf 0.95}
                                                      & \scalebox{0.9}[0.75]{\bf 0.93}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.74}
                                                                        & \scalebox{0.7}{0.68}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.84}
                                                                                       & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                                         & \scalebox{0.7}{0.72}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.79}
                              & \scalebox{0.9}[0.75]{\bf 0.81}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.97}
                                                  & \scalebox{0.9}[0.75]{\bf 0.95}
                                                    & \scalebox{0.9}[0.75]{\bf 0.92}
                                                      & \scalebox{0.9}[0.75]{\bf 0.9}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                      & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                        & \scalebox{0.7}{0.71}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.85}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                                       & \scalebox{0.7}{0.71}
                                                                                         & \scalebox{0.7}{0.65}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.93}
                            & \scalebox{0.9}[0.75]{\bf 0.89}
                              & \scalebox{0.9}[0.75]{\bf 0.86}
                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.96}
                                                  & \scalebox{0.9}[0.75]{\bf 0.93}
                                                    & \scalebox{0.9}[0.75]{\bf 0.9}
                                                      & \scalebox{0.9}[0.75]{\bf 0.88}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                      & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                        & \scalebox{0.7}{0.7}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.88}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                                     & \scalebox{0.7}{0.7}
                                                                                       & \scalebox{0.7}{0.63}
                                                                                         & \scalebox{0.7}{0.61}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$0.75$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.79}
                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.98}
                                                  & \scalebox{0.9}[0.75]{\bf 0.97}
                                                    & \scalebox{0.9}[0.75]{\bf 0.95}
                                                      & \scalebox{0.9}[0.75]{\bf 0.93}
                                                                & \scalebox{0.9}[0.75]{\bf 0.84}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{\bf 0.73}
                                                                        & \scalebox{0.7}{0.67}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                                       & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                         & \scalebox{0.7}{0.71}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.79}
                              & \scalebox{0.9}[0.75]{\bf 0.81}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.97}
                                                  & \scalebox{0.9}[0.75]{\bf 0.95}
                                                    & \scalebox{0.9}[0.75]{\bf 0.92}
                                                      & \scalebox{0.9}[0.75]{\bf 0.9}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                      & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                        & \scalebox{0.7}{0.71}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.85}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                       & \scalebox{0.7}{0.7}
                                                                                         & \scalebox{0.7}{0.65}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.93}
                            & \scalebox{0.9}[0.75]{\bf 0.89}
                              & \scalebox{0.9}[0.75]{\bf 0.86}
                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.96}
                                                  & \scalebox{0.9}[0.75]{\bf 0.93}
                                                    & \scalebox{0.9}[0.75]{\bf 0.9}
                                                      & \scalebox{0.9}[0.75]{\bf 0.88}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.74}
                                                                        & \scalebox{0.7}{0.69}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.9}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                     & \scalebox{0.7}{0.69}
                                                                                       & \scalebox{0.7}{0.63}
                                                                                         & \scalebox{0.7}{0.61}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$1$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.78}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.78}
                                & \scalebox{0.9}[0.75]{\bf 0.79}
                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.96}
                                                  & \scalebox{0.9}[0.75]{\bf 0.93}
                                                    & \scalebox{0.9}[0.75]{\bf 0.88}
                                                      & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.72}
                                                                        & \scalebox{0.7}{0.67}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                                       & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                         & \scalebox{0.7}{0.69}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.8}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.93}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                      & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                        & \scalebox{0.7}{0.7}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                                     & \scalebox{0.7}{0.74}
                                                                                       & \scalebox{0.7}{0.66}
                                                                                         & \scalebox{0.7}{0.61}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.87}
                            & \scalebox{0.9}[0.75]{\bf 0.82}
                              & \scalebox{0.9}[0.75]{\bf 0.83}
                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                              & \scalebox{0.9}[0.75]{\bf 0.97}
                                                & \scalebox{0.9}[0.75]{\bf 0.91}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.74}
                                                                        & \scalebox{0.7}{0.69}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.86}
                                                                                   & \scalebox{0.7}{0.71}
                                                                                     & \scalebox{0.7}{0.61}
                                                                                       & \scalebox{0.7}{0.57}
                                                                                         & \scalebox{0.7}{0.55}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$1.25$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.78}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.78}
                                & \scalebox{0.9}[0.75]{\bf 0.79}
                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.96}
                                                  & \scalebox{0.9}[0.75]{\bf 0.93}
                                                    & \scalebox{0.9}[0.75]{\bf 0.88}
                                                      & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                & \scalebox{0.9}[0.75]{\bf 0.84}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                      & \scalebox{0.7}{0.73}
                                                                        & \scalebox{0.7}{0.67}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                                       & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                         & \scalebox{0.7}{0.69}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.8}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.93}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                      & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                        & \scalebox{0.7}{0.7}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.95}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                                     & \scalebox{0.7}{0.74}
                                                                                       & \scalebox{0.7}{0.67}
                                                                                         & \scalebox{0.7}{0.61}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.87}
                            & \scalebox{0.9}[0.75]{\bf 0.82}
                              & \scalebox{0.9}[0.75]{\bf 0.83}
                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                              & \scalebox{0.9}[0.75]{\bf 0.97}
                                                & \scalebox{0.9}[0.75]{\bf 0.91}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.74}
                                                                        & \scalebox{0.7}{0.68}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.86}
                                                                                   & \scalebox{0.7}{0.7}
                                                                                     & \scalebox{0.7}{0.63}
                                                                                       & \scalebox{0.7}{0.59}
                                                                                         & \scalebox{0.7}{0.56}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$1.5$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.78}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.78}
                                & \scalebox{0.9}[0.75]{\bf 0.79}
                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.96}
                                                  & \scalebox{0.9}[0.75]{\bf 0.93}
                                                    & \scalebox{0.9}[0.75]{\bf 0.88}
                                                      & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                & \scalebox{0.9}[0.75]{\bf 0.84}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                      & \scalebox{0.7}{0.72}
                                                                        & \scalebox{0.7}{0.65}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                                       & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                         & \scalebox{0.7}{0.69}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.8}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.93}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                      & \scalebox{0.7}{0.74}
                                                                        & \scalebox{0.7}{0.68}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                                     & \scalebox{0.7}{0.72}
                                                                                       & \scalebox{0.7}{0.67}
                                                                                         & \scalebox{0.7}{0.62}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.87}
                            & \scalebox{0.9}[0.75]{\bf 0.82}
                              & \scalebox{0.9}[0.75]{\bf 0.83}
                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                              & \scalebox{0.9}[0.75]{\bf 0.97}
                                                & \scalebox{0.9}[0.75]{\bf 0.91}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.73}
                                                                        & \scalebox{0.7}{0.67}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.85}
                                                                                   & \scalebox{0.7}{0.69}
                                                                                     & \scalebox{0.7}{0.62}
                                                                                       & \scalebox{0.7}{0.59}
                                                                                         & \scalebox{0.7}{0.56}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$1.75$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.78}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.78}
                                & \scalebox{0.9}[0.75]{\bf 0.79}
                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.96}
                                                  & \scalebox{0.9}[0.75]{\bf 0.93}
                                                    & \scalebox{0.9}[0.75]{\bf 0.88}
                                                      & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.72}
                                                                        & \scalebox{0.7}{0.65}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                                       & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                         & \scalebox{0.7}{0.69}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.8}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.93}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.74}
                                                                        & \scalebox{0.7}{0.66}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.93}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                                     & \scalebox{0.7}{0.73}
                                                                                       & \scalebox{0.7}{0.67}
                                                                                         & \scalebox{0.7}{0.63}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.87}
                            & \scalebox{0.9}[0.75]{\bf 0.82}
                              & \scalebox{0.9}[0.75]{\bf 0.83}
                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                              & \scalebox{0.9}[0.75]{\bf 0.97}
                                                & \scalebox{0.9}[0.75]{\bf 0.91}
                                                  & \scalebox{0.9}[0.75]{\bf 0.87}
                                                    & \scalebox{0.9}[0.75]{\bf 0.81}
                                                      & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.72}
                                                                        & \scalebox{0.7}{0.66}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                                   & \scalebox{0.7}{0.68}
                                                                                     & \scalebox{0.7}{0.61}
                                                                                       & \scalebox{0.7}{0.6}
                                                                                         & \scalebox{0.7}{0.59}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$2$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.76}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.95}
                                                  & \scalebox{0.9}[0.75]{\bf 0.89}
                                                    & \scalebox{0.9}[0.75]{\bf 0.83}
                                                      & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.72}
                                                                        & \scalebox{0.7}{0.65}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.89}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                                       & \scalebox{0.7}{0.72}
                                                                                         & \scalebox{0.7}{0.64}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.84}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.89}
                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                    & \scalebox{0.7}{0.71}
                                                      & \scalebox{0.7}{0.69}
                                                                & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.72}
                                                                        & \scalebox{0.7}{0.64}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.93}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                                     & \scalebox{0.7}{0.69}
                                                                                       & \scalebox{0.7}{0.65}
                                                                                         & \scalebox{0.7}{0.6}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.85}
                            & \scalebox{0.9}[0.75]{\bf 0.83}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.75}
                                              & \scalebox{0.9}[0.75]{\bf 0.95}
                                                & \scalebox{0.9}[0.75]{\bf 0.88}
                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                    & \scalebox{0.7}{0.72}
                                                      & \scalebox{0.7}{0.61}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.71}
                                                                        & \scalebox{0.7}{0.65}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                                   & \scalebox{0.7}{0.64}
                                                                                     & \scalebox{0.7}{0.59}
                                                                                       & \scalebox{0.7}{0.58}
                                                                                         & \scalebox{0.7}{0.57}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$2.25$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.76}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.95}
                                                  & \scalebox{0.9}[0.75]{\bf 0.89}
                                                    & \scalebox{0.9}[0.75]{\bf 0.83}
                                                      & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.72}
                                                                        & \scalebox{0.7}{0.65}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.88}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                                       & \scalebox{0.7}{0.72}
                                                                                         & \scalebox{0.7}{0.63}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.84}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.89}
                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                    & \scalebox{0.7}{0.71}
                                                      & \scalebox{0.7}{0.69}
                                                                & \scalebox{0.9}[0.75]{\bf 0.83}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.7}
                                                                        & \scalebox{0.7}{0.62}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.93}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                                     & \scalebox{0.7}{0.7}
                                                                                       & \scalebox{0.7}{0.65}
                                                                                         & \scalebox{0.7}{0.6}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.85}
                            & \scalebox{0.9}[0.75]{\bf 0.83}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.75}
                                              & \scalebox{0.9}[0.75]{\bf 0.95}
                                                & \scalebox{0.9}[0.75]{\bf 0.88}
                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                    & \scalebox{0.7}{0.72}
                                                      & \scalebox{0.7}{0.61}
                                                                & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.71}
                                                                        & \scalebox{0.7}{0.64}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                                   & \scalebox{0.7}{0.65}
                                                                                     & \scalebox{0.7}{0.6}
                                                                                       & \scalebox{0.7}{0.6}
                                                                                         & \scalebox{0.7}{0.56}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$2.5$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.76}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.95}
                                                  & \scalebox{0.9}[0.75]{\bf 0.89}
                                                    & \scalebox{0.9}[0.75]{\bf 0.83}
                                                      & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                      & \scalebox{0.7}{0.71}
                                                                        & \scalebox{0.7}{0.64}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.87}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                       & \scalebox{0.7}{0.69}
                                                                                         & \scalebox{0.7}{0.61}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.84}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.89}
                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                    & \scalebox{0.7}{0.71}
                                                      & \scalebox{0.7}{0.69}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                      & \scalebox{0.7}{0.69}
                                                                        & \scalebox{0.7}{0.6}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.92}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                     & \scalebox{0.7}{0.69}
                                                                                       & \scalebox{0.7}{0.63}
                                                                                         & \scalebox{0.7}{0.58}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.85}
                            & \scalebox{0.9}[0.75]{\bf 0.83}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.75}
                                              & \scalebox{0.9}[0.75]{\bf 0.95}
                                                & \scalebox{0.9}[0.75]{\bf 0.88}
                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                    & \scalebox{0.7}{0.72}
                                                      & \scalebox{0.7}{0.61}
                                                                & \scalebox{0.9}[0.75]{\bf 0.82}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                      & \scalebox{0.7}{0.69}
                                                                        & \scalebox{0.7}{0.62}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                                   & \scalebox{0.7}{0.63}
                                                                                     & \scalebox{0.7}{0.59}
                                                                                       & \scalebox{0.7}{0.59}
                                                                                         & \scalebox{0.7}{0.56}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$2.75$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.77}
                              & \scalebox{0.9}[0.75]{\bf 0.76}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.99}
                                                & \scalebox{0.9}[0.75]{\bf 0.95}
                                                  & \scalebox{0.9}[0.75]{\bf 0.89}
                                                    & \scalebox{0.9}[0.75]{\bf 0.83}
                                                      & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                      & \scalebox{0.7}{0.69}
                                                                        & \scalebox{0.7}{0.61}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.87}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                       & \scalebox{0.7}{0.66}
                                                                                         & \scalebox{0.7}{0.59}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.8}
                            & \scalebox{0.9}[0.75]{\bf 0.84}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.76}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.89}
                                                  & \scalebox{0.9}[0.75]{\bf 0.81}
                                                    & \scalebox{0.7}{0.71}
                                                      & \scalebox{0.7}{0.69}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                      & \scalebox{0.7}{0.68}
                                                                        & \scalebox{0.7}{0.6}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.92}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                     & \scalebox{0.7}{0.69}
                                                                                       & \scalebox{0.7}{0.63}
                                                                                         & \scalebox{0.7}{0.58}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.85}
                            & \scalebox{0.9}[0.75]{\bf 0.83}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.78}
                                  & \scalebox{0.9}[0.75]{\bf 0.75}
                                              & \scalebox{0.9}[0.75]{\bf 0.95}
                                                & \scalebox{0.9}[0.75]{\bf 0.88}
                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                    & \scalebox{0.7}{0.72}
                                                      & \scalebox{0.7}{0.61}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                      & \scalebox{0.7}{0.69}
                                                                        & \scalebox{0.7}{0.61}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                                   & \scalebox{0.7}{0.63}
                                                                                     & \scalebox{0.7}{0.6}
                                                                                       & \scalebox{0.7}{0.6}
                                                                                         & \scalebox{0.7}{0.56}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$3$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.78}
                            & \scalebox{0.9}[0.75]{\bf 0.79}
                              & \scalebox{0.9}[0.75]{\bf 0.79}
                                & \scalebox{0.9}[0.75]{\bf 0.76}
                                  & \scalebox{0.7}{0.72}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.94}
                                                  & \scalebox{0.9}[0.75]{\bf 0.86}
                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                      & \scalebox{0.7}{0.7}
                                                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                      & \scalebox{0.7}{0.69}
                                                                        & \scalebox{0.7}{0.59}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.87}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                       & \scalebox{0.7}{0.66}
                                                                                         & \scalebox{0.7}{0.58}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.81}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.7}{0.73}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.87}
                                                  & \scalebox{0.7}{0.73}
                                                    & \scalebox{0.7}{0.68}
                                                      & \scalebox{0.7}{0.63}
                                                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.7}{0.74}
                                                                      & \scalebox{0.7}{0.66}
                                                                        & \scalebox{0.7}{0.57}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.92}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                     & \scalebox{0.7}{0.69}
                                                                                       & \scalebox{0.7}{0.63}
                                                                                         & \scalebox{0.7}{0.56}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.87}
                            & \scalebox{0.9}[0.75]{\bf 0.8}
                              & \scalebox{0.9}[0.75]{\bf 0.78}
                                & \scalebox{0.9}[0.75]{\bf 0.75}
                                  & \scalebox{0.7}{0.71}
                                              & \scalebox{0.9}[0.75]{\bf 0.94}
                                                & \scalebox{0.9}[0.75]{\bf 0.84}
                                                  & \scalebox{0.7}{0.72}
                                                    & \scalebox{0.7}{0.61}
                                                      & \scalebox{0.7}{0.58}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                      & \scalebox{0.7}{0.68}
                                                                        & \scalebox{0.7}{0.6}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                   & \scalebox{0.7}{0.62}
                                                                                     & \scalebox{0.7}{0.61}
                                                                                       & \scalebox{0.7}{0.6}
                                                                                         & \scalebox{0.7}{0.55}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$3.25$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.78}
                            & \scalebox{0.9}[0.75]{\bf 0.79}
                              & \scalebox{0.9}[0.75]{\bf 0.79}
                                & \scalebox{0.9}[0.75]{\bf 0.76}
                                  & \scalebox{0.7}{0.72}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.94}
                                                  & \scalebox{0.9}[0.75]{\bf 0.86}
                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                      & \scalebox{0.7}{0.7}
                                                                & \scalebox{0.9}[0.75]{\bf 0.8}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                      & \scalebox{0.7}{0.68}
                                                                        & \scalebox{0.7}{0.57}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.88}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                                       & \scalebox{0.7}{0.65}
                                                                                         & \scalebox{0.7}{0.55}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.81}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.7}{0.73}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.87}
                                                  & \scalebox{0.7}{0.73}
                                                    & \scalebox{0.7}{0.68}
                                                      & \scalebox{0.7}{0.63}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.7}{0.74}
                                                                      & \scalebox{0.7}{0.65}
                                                                        & \scalebox{0.7}{0.55}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.92}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                     & \scalebox{0.7}{0.69}
                                                                                       & \scalebox{0.7}{0.62}
                                                                                         & \scalebox{0.7}{0.53}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.87}
                            & \scalebox{0.9}[0.75]{\bf 0.8}
                              & \scalebox{0.9}[0.75]{\bf 0.78}
                                & \scalebox{0.9}[0.75]{\bf 0.75}
                                  & \scalebox{0.7}{0.71}
                                              & \scalebox{0.9}[0.75]{\bf 0.94}
                                                & \scalebox{0.9}[0.75]{\bf 0.84}
                                                  & \scalebox{0.7}{0.72}
                                                    & \scalebox{0.7}{0.61}
                                                      & \scalebox{0.7}{0.58}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.7}{0.74}
                                                                      & \scalebox{0.7}{0.67}
                                                                        & \scalebox{0.7}{0.58}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.77}
                                                                                   & \scalebox{0.7}{0.61}
                                                                                     & \scalebox{0.7}{0.61}
                                                                                       & \scalebox{0.7}{0.59}
                                                                                         & \scalebox{0.7}{0.52}
\\
\hline
\multirow{3}{*}{\scalebox{0.7}{$3.5$}}
   & \scalebox{0.75}{\hspace*{-0.1in}$50$} 
                          & \scalebox{0.9}[0.75]{\bf 0.78}
                            & \scalebox{0.9}[0.75]{\bf 0.79}
                              & \scalebox{0.9}[0.75]{\bf 0.79}
                                & \scalebox{0.9}[0.75]{\bf 0.76}
                                  & \scalebox{0.7}{0.72}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.94}
                                                  & \scalebox{0.9}[0.75]{\bf 0.86}
                                                    & \scalebox{0.9}[0.75]{\bf 0.77}
                                                      & \scalebox{0.7}{0.7}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                      & \scalebox{0.7}{0.67}
                                                                        & \scalebox{0.7}{0.55}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.94}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.87}
                                                                                     & \scalebox{0.9}[0.75]{\bf 0.75}
                                                                                       & \scalebox{0.7}{0.64}
                                                                                         & \scalebox{0.7}{0.54}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$100$} 
                          & \scalebox{0.9}[0.75]{\bf 0.79}
                            & \scalebox{0.9}[0.75]{\bf 0.81}
                              & \scalebox{0.9}[0.75]{\bf 0.8}
                                & \scalebox{0.9}[0.75]{\bf 0.77}
                                  & \scalebox{0.7}{0.73}
                                              & \scalebox{0.9}[0.75]{\bf 0.98}
                                                & \scalebox{0.9}[0.75]{\bf 0.87}
                                                  & \scalebox{0.7}{0.73}
                                                    & \scalebox{0.7}{0.68}
                                                      & \scalebox{0.7}{0.63}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.79}
                                                                    & \scalebox{0.7}{0.73}
                                                                      & \scalebox{0.7}{0.64}
                                                                        & \scalebox{0.7}{0.54}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.92}
                                                                                   & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                     & \scalebox{0.7}{0.69}
                                                                                       & \scalebox{0.7}{0.62}
                                                                                         & \scalebox{0.7}{0.52}
\\
   & \scalebox{0.75}{\hspace*{-0.1in}$300$} 
                          & \scalebox{0.9}[0.75]{\bf 0.87}
                            & \scalebox{0.9}[0.75]{\bf 0.8}
                              & \scalebox{0.9}[0.75]{\bf 0.78}
                                & \scalebox{0.9}[0.75]{\bf 0.75}
                                  & \scalebox{0.7}{0.71}
                                              & \scalebox{0.9}[0.75]{\bf 0.94}
                                                & \scalebox{0.9}[0.75]{\bf 0.84}
                                                  & \scalebox{0.7}{0.72}
                                                    & \scalebox{0.7}{0.61}
                                                      & \scalebox{0.7}{0.58}
                                                                & \scalebox{0.9}[0.75]{\bf 0.81}
                                                                  & \scalebox{0.9}[0.75]{\bf 0.78}
                                                                    & \scalebox{0.7}{0.73}
                                                                      & \scalebox{0.7}{0.65}
                                                                        & \scalebox{0.7}{0.56}
                                                                                 & \scalebox{0.9}[0.75]{\bf 0.76}
                                                                                   & \scalebox{0.7}{0.61}
                                                                                     & \scalebox{0.7}{0.61}
                                                                                       & \scalebox{0.7}{0.59}
                                                                                         & \scalebox{0.7}{0.52}
\\
\bottomrule
\end{tabular}
%%%
}
\end{center}
%
\end{table}
%
\renewcommand{\tabcolsep}{6pt}
%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% END table for sharp increase of xi at gamma=0.1 for homogeneous dense ER and SF networks
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
































\subsubsection{Homogeneous in-arborescence networks}

Homogeneous in-arborescence networks under coordinated shocks exhibited a {\em sharp} increase in stability 
as the ratio $\frac{\E}{\I}$ of the total external asset to the total interbank exposure the system is increased beyond a particular threshold {\em provided the equity to asset ratio $\gamma$ 
was approximately $\nicefrac{\Phi}{2}$}.
For example, 
for a 50-node homogeneous in-arborescence network under coordinated shock, $\xi$ exhibited a sharp decrease from 0.76 to 0.18 
for $\frac{\E}{\I}\in\big[0.75,1\big]$, $\mathcal{K}=0.1$, $\Phi=0.5$ and $\gamma=0.25=\nicefrac{\Phi}{2}$; 
see {\em supplemental} {\sc Fig}.~\ref{newfig4} for a visual illustration.

To investigate the global extent of such a sharp decrease of $\xi$ around a threshold value of $\frac{\E}{\I}$ in the range $\big[0.5,1\big]$ with $\gamma\approx\nicefrac{\Phi}{2}$, we 
computed, for each type of shocking mechanism, and for each values of the parameters $n$, $\Phi$, $\gamma\approx\nicefrac{\Phi}{2}$, and $\kappa$
of the homogeneous in-arborescence network, the ratio 
%
\[
\Delta(n,\Phi,\gamma,\mathcal{K})
=
\dfrac
{
\displaystyle
\max_{\substack{ 0.5\leq \frac{\E}{\I} \leq 1 \\ } } \big\{ \xi \big\}- \min_{\substack{ 0.5\leq \frac{\E}{\I} \leq 1 } } \big\{ \xi \big\}
}
{
\displaystyle
\max_{\substack{ \text{entire range of } \E } } \big\{ \xi \big\}- \min_{\substack{ \text{entire range of } \E  } } \big\{ \xi \big\}
}
\]
%
that provides the {\em maximum} percentage of the total change of the vulnerability index that occurred within this range of $\frac{\E}{\I}$. 
If the growth of $\xi$ with respect to $\nicefrac{\E}{\I}$ was uniform or near uniform over the entire range of $\frac{\E}{\I}$, $\Delta$ would be approximately 
$\delta=\frac{1-0.5}{3.5-0.25}\approx 0.16$; thus, any value of $\Delta$ significantly higher than $\delta$ indicates a sharp transition 
within the above-mentioned range of $\nicefrac{\E}{\I}$. As Table~\ref{table11} shows, when $\gamma=\nicefrac{\Phi}{2}$ 
a {\em significant} majority of the entries are coordinated shocks and many entries under idiosyncratic shocks are at least $2\,\delta$. 




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% table for sharp increase of xi at E=0.75 for homogeneous in-arborescence networks
\begin{table}
%
\caption[]{Values of 
%
$
\displaystyle
\Delta(n,\Phi,\gamma,\mathcal{K})
=
\dfrac
{
\displaystyle
\max_{\substack{ 0.5\leq E/I \leq 1 \\ } } \big\{ \xi \big\}- \min_{\substack{ 0.5\leq E/I\leq 1 } } \big\{ \xi \big\}
}
{
\displaystyle
\max_{\substack{ \text{entire range of } E } } \big\{ \xi \big\}- \min_{\substack{ \text{entire range of } E  } } \big\{ \xi \big\}
}
$
%
for homogeneous in-arborescence networks. Entries that are at least $2\times 0.16$ are shown in {\bf boldface black}.
Entries that are at least $\frac{3}{2}\times 0.16$ are shown in {\bf\color{darkgray} boldface gray}.
}
%
\label{table11}
%
\begin{center}
%
\scalebox{0.75}[0.65]
{%%\tiny
\setlength{\extrarowheight}{0ex}
\begin{tabular}{c | c | c | l | l l l l l l l l l }
%%%\vspace*{-1.4in}
\toprule
%
\multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{9}{c}{\hspace*{-0.1in}\Large \scalebox{8.5}[1.2]{${\leftarrow}$}$\pmb{\mathcal{K}}$\scalebox{8.5}[1.2]{${\rightarrow}$}}
\\
\multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} 
     & \normalsize 0.1 & \normalsize 0.2 & \normalsize 0.3 & \normalsize 0.4 & \normalsize 0.5 & \normalsize 0.6 & \normalsize 0.7 & \normalsize 0.8 & \normalsize 0.9 
\\
\hline
\multirow{30}{*}{\normalsize \begin{tabular}{c} Coordinated \\ shock \end{tabular}} & 
    \multirow{10}{*}{\normalsize \begin{tabular}{c} $|V|$ \\ $=$ \\ 50 \end{tabular} } & 
      \multirow{2}{*}{\normalsize $\Phi=0.5$} 
         & \scalebox{1   }[1]{$\gamma=0.25$} 
         & \scalebox{1.1}[1.1]{\bf 0.87} & \scalebox{1.1}[1.1]{\bf 0.86} & \scalebox{1.1}[1.1]{\bf 0.84} & \scalebox{1.1}[1.1]{\bf 0.83} & \scalebox{1.1}[1.1]{\bf 0.83} & \scalebox{1.1}[1.1]{\bf 0.83} & \scalebox{1.1}[1.1]{\bf 0.83} & \scalebox{1.1}[1.1]{\bf 0.83} & \scalebox{1.1}[1.1]{\bf 0.83} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.3$}
         & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 0.99} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.6$} 
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1}[1]{\bf\color{darkgray} 0.27} & \scalebox{1.1}[1.1]{\bf 0.49} & \scalebox{1.1}[1.1]{\bf 0.52} & \scalebox{1.1}[1.1]{\bf 0.52} & \scalebox{1.1}[1.1]{\bf 0.52} & \scalebox{1.1}[1.1]{\bf 0.52} & \scalebox{1.1}[1.1]{\bf 0.52} & \scalebox{1.1}[1.1]{\bf 0.52} & \scalebox{1.1}[1.1]{\bf 0.52} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.27} & \scalebox{1.1}[1.1]{\bf 0.51} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.37} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.7$} 
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.27} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1.1}[1.1]{\bf 0.59} & \scalebox{1.1}[1.1]{\bf 0.64} & \scalebox{1.1}[1.1]{\bf 0.65} & \scalebox{1.1}[1.1]{\bf 0.65} & \scalebox{1.1}[1.1]{\bf 0.65} & \scalebox{1.1}[1.1]{\bf 0.65} & \scalebox{1.1}[1.1]{\bf 0.65} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.30} & \scalebox{1.1}[1.1]{\bf 0.34} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.8$} 
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.24} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1.1}[1.1]{\bf 0.45} & \scalebox{1.1}[1.1]{\bf 0.43} & \scalebox{1.1}[1.1]{\bf 0.41} & \scalebox{1.1}[1.1]{\bf 0.40} & \scalebox{1.1}[1.1]{\bf 0.40} & \scalebox{1.1}[1.1]{\bf 0.40} & \scalebox{1.1}[1.1]{\bf 0.40} & \scalebox{1.1}[1.1]{\bf 0.40} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.9$} 
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.24} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.54} & \scalebox{1.1}[1.1]{\bf 0.56} & \scalebox{1.1}[1.1]{\bf 0.56} & \scalebox{1.1}[1.1]{\bf 0.56} & \scalebox{1.1}[1.1]{\bf 0.56} & \scalebox{1.1}[1.1]{\bf 0.56} & \scalebox{1.1}[1.1]{\bf 0.56} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.5$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.28} & \scalebox{1.1}[1.1]{\bf 0.38} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.34} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} 
\\
\cline{2-13}
&
    \multirow{10}{*}{\normalsize \begin{tabular}{c} $|V|$ \\ $=$ \\ 100 \end{tabular}}
&
      \multirow{2}{*}{\normalsize $\Phi=0.5$} 
         & \scalebox{1   }[1]{$\gamma=0.25$} 
         & \scalebox{1.1}[1.1]{\bf 0.95} & \scalebox{1.1}[1.1]{\bf 0.94} & \scalebox{1.1}[1.1]{\bf 0.94} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1.1}[1.1]{\bf 0.98} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 1.00} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.6$} 
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1.1}[1.1]{\bf 0.39} & \scalebox{1}[1]{\color{darkgray}\bf 0.27} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1}[1]{\color{darkgray}\bf 0.31} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1}[1]{\color{darkgray}\bf 0.24} & \scalebox{1}[1]{\color{darkgray}\bf 0.28} & \scalebox{1}[1]{\color{darkgray}\bf 0.30} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.32} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.7$} 
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1.1}[1.1]{\bf 0.39} & \scalebox{1.1}[1.1]{\bf 0.57} & \scalebox{1.1}[1.1]{\bf 0.67} & \scalebox{1.1}[1.1]{\bf 0.69} & \scalebox{1.1}[1.1]{\bf 0.69} & \scalebox{1.1}[1.1]{\bf 0.69} & \scalebox{1.1}[1.1]{\bf 0.69} & \scalebox{1.1}[1.1]{\bf 0.69} & \scalebox{1.1}[1.1]{\bf 0.69} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1.1}[1.1]{\bf 0.36} & \scalebox{1.1}[1.1]{\bf 0.44} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.42} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.8$} 
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1.1}[1.1]{\bf 0.36} & \scalebox{1.1}[1.1]{\bf 0.49} & \scalebox{1.1}[1.1]{\bf 0.54} & \scalebox{1.1}[1.1]{\bf 0.53} & \scalebox{1.1}[1.1]{\bf 0.53} & \scalebox{1.1}[1.1]{\bf 0.53} & \scalebox{1.1}[1.1]{\bf 0.53} & \scalebox{1.1}[1.1]{\bf 0.53} & \scalebox{1.1}[1.1]{\bf 0.53} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.46} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1.1}[1.1]{\bf 0.48} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.9$} 
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1.1}[1.1]{\bf 0.39} & \scalebox{1.1}[1.1]{\bf 0.56} & \scalebox{1.1}[1.1]{\bf 0.66} & \scalebox{1.1}[1.1]{\bf 0.67} & \scalebox{1.1}[1.1]{\bf 0.67} & \scalebox{1.1}[1.1]{\bf 0.67} & \scalebox{1.1}[1.1]{\bf 0.67} & \scalebox{1.1}[1.1]{\bf 0.67} & \scalebox{1.1}[1.1]{\bf 0.67} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.5$} 
         & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.47} 
\\
\cline{2-13}
&
    \multirow{10}{*}{\normalsize \begin{tabular}{c} $|V|$ \\ $=$ \\ 300 \end{tabular}}
&
      \multirow{2}{*}{\normalsize $\Phi=0.5$} 
         & \scalebox{1   }[1]{$\gamma=0.25$} 
         & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.94} & \scalebox{1.1}[1.1]{\bf 0.94} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.93} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1.1}[1.1]{\bf 0.99} & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 1.00   } 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.6$} 
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1.1}[1.1]{\bf 0.39} & \scalebox{1}[1]{\color{darkgray}\bf 0.27} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.31} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.16} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.7$} 
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1.1}[1.1]{\bf 0.40} & \scalebox{1.1}[1.1]{\bf 0.53} & \scalebox{1.1}[1.1]{\bf 0.61} & \scalebox{1.1}[1.1]{\bf 0.62} & \scalebox{1.1}[1.1]{\bf 0.62} & \scalebox{1.1}[1.1]{\bf 0.62} & \scalebox{1.1}[1.1]{\bf 0.62} & \scalebox{1.1}[1.1]{\bf 0.62} & \scalebox{1.1}[1.1]{\bf 0.62} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1.1}[1.1]{\bf 0.34} & \scalebox{1.1}[1.1]{\bf 0.36} & \scalebox{1.1}[1.1]{\bf 0.34} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1.1}[1.1]{\bf 0.33} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.8$} 
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1.1}[1.1]{\bf 0.38} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.50 } & \scalebox{1.1}[1.1]{\bf 0.50 } & \scalebox{1.1}[1.1]{\bf 0.50 } & \scalebox{1.1}[1.1]{\bf 0.50 } & \scalebox{1.1}[1.1]{\bf 0.50 } & \scalebox{1.1}[1.1]{\bf 0.50 } & \scalebox{1.1}[1.1]{\bf 0.50 } 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1.1}[1.1]{\bf 0.39} & \scalebox{1.1}[1.1]{\bf 0.43} & \scalebox{1.1}[1.1]{\bf 0.42} & \scalebox{1.1}[1.1]{\bf 0.40 } & \scalebox{1.1}[1.1]{\bf 0.40 } & \scalebox{1.1}[1.1]{\bf 0.40 } & \scalebox{1.1}[1.1]{\bf 0.40 } & \scalebox{1.1}[1.1]{\bf 0.40 } & \scalebox{1.1}[1.1]{\bf 0.40 } 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.9$} 
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1.1}[1.1]{\bf 0.40 } & \scalebox{1.1}[1.1]{\bf 0.53} & \scalebox{1.1}[1.1]{\bf 0.60 } & \scalebox{1.1}[1.1]{\bf 0.61} & \scalebox{1.1}[1.1]{\bf 0.61} & \scalebox{1.1}[1.1]{\bf 0.61} & \scalebox{1.1}[1.1]{\bf 0.61} & \scalebox{1.1}[1.1]{\bf 0.61} & \scalebox{1.1}[1.1]{\bf 0.61} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.5$} 
         & \scalebox{1.1}[1.1]{\bf 0.39} & \scalebox{1.1}[1.1]{\bf 0.44} & \scalebox{1.1}[1.1]{\bf 0.44} & \scalebox{1.1}[1.1]{\bf 0.43} & \scalebox{1.1}[1.1]{\bf 0.43} & \scalebox{1.1}[1.1]{\bf 0.43} & \scalebox{1.1}[1.1]{\bf 0.43} & \scalebox{1.1}[1.1]{\bf 0.43} & \scalebox{1.1}[1.1]{\bf 0.43} 
\\
\hline
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\multirow{30}{*}{\normalsize \begin{tabular}{c} Idiosyncratic \\ shock \end{tabular}} & 
    \multirow{10}{*}{\normalsize \begin{tabular}{c} $|V|$ \\ $=$ \\ 50 \end{tabular}}
&
      \multirow{2}{*}{\normalsize $\Phi=0.5$} 
         & \scalebox{1   }[1]{$\gamma=0.25$} 
         & \scalebox{1.1}[1.1]{\bf 0.95} & \scalebox{1.1}[1.1]{\bf 0.95} & \scalebox{1.1}[1.1]{\bf 0.95} & \scalebox{1.1}[1.1]{\bf 0.76} & \scalebox{1.1}[1.1]{\bf 0.77} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.11} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1.1}[1.1]{\bf 0.95} & \scalebox{1.1}[1.1]{\bf 0.95} & \scalebox{1.1}[1.1]{\bf 0.93} & \scalebox{1.1}[1.1]{\bf 0.99} & \scalebox{1.1}[1.1]{\bf 0.76} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.23} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.6$} 
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1.1}[1.1]{\bf 0.32} & \scalebox{1.1}[1.1]{\bf 0.47} & \scalebox{1.1}[1.1]{\bf 0.48} & \scalebox{1}[1]{\color{darkgray}\bf 0.21} & \scalebox{1.1}[1.1]{\bf 0.35} & \scalebox{1.1}[1.1]{\bf 0.39} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.27} & \scalebox{1}[1]{\color{darkgray}\bf 0.30} & \scalebox{1.1}[1.1]{\bf 0.38} & \scalebox{1}[1]{\color{darkgray}\bf 0.27} & \scalebox{1}[1]{\color{darkgray}\bf 0.24} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.16} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.7$} 
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.15} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.26} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.11} & \scalebox{1}[1]{\color{darkgray}\bf 0.15} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.25} & \scalebox{1}[1]{\color{darkgray}\bf 0.17} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.09} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.8$} 
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.05} & \scalebox{1}[1]{\color{darkgray}\bf 0.09} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.21} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.02} & \scalebox{1}[1]{\color{darkgray}\bf 0.17} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.27} & \scalebox{1}[1]{\color{darkgray}\bf 0.17} & \scalebox{1}[1]{\color{darkgray}\bf 0.19} & \scalebox{1}[1]{\color{darkgray}\bf 0.05} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.9$} 
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.09} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.20 } & \scalebox{1}[1]{\color{darkgray}\bf 0.21} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.02} & \scalebox{1}[1]{\color{darkgray}\bf 0.17} & \scalebox{1}[1]{\color{darkgray}\bf 0.17} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.5$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.24} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } 
\\
\cline{2-13}
&
    \multirow{10}{*}{\normalsize \begin{tabular}{c} $|V|$ \\ $=$ \\ 100 \end{tabular}}
&
      \multirow{2}{*}{\normalsize $\Phi=0.5$} 
         & \scalebox{1   }[1]{$\gamma=0.25$} 
         & \scalebox{1.1}[1.1]{\bf 0.98} & \scalebox{1.1}[1.1]{\bf 0.96} & \scalebox{1.1}[1.1]{\bf 0.98} & \scalebox{1.1}[1.1]{\bf 0.96} & \scalebox{1.1}[1.1]{\bf 0.67} & \scalebox{1.1}[1.1]{\bf 0.37} & \scalebox{1}[1]{\color{darkgray}\bf 0.16} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.16} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1.1}[1.1]{\bf 0.99} & \scalebox{1.1}[1.1]{\bf 1.00} & \scalebox{1.1}[1.1]{\bf 0.95} & \scalebox{1.1}[1.1]{\bf 0.99} & \scalebox{1.1}[1.1]{\bf 0.71} & \scalebox{1}[1]{\color{darkgray}\bf 0.31} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.11} & \scalebox{1}[1]{\color{darkgray}\bf 0.26} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.6$} 
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.15} & \scalebox{1}[1]{\color{darkgray}\bf 0.3 } & \scalebox{1.1}[1.1]{\bf 0.44} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.22} & \scalebox{1}[1]{\color{darkgray}\bf 0.16} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.29} & \scalebox{1}[1]{\color{darkgray}\bf 0.30} & \scalebox{1}[1]{\color{darkgray}\bf 0.17} & \scalebox{1.1}[1.1]{\bf 0.33} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.7$} 
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.02} & \scalebox{1}[1]{\color{darkgray}\bf 0.11} & \scalebox{1}[1]{\color{darkgray}\bf 0.09} & \scalebox{1}[1]{\color{darkgray}\bf 0.23} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.01} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.05} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.02} & \scalebox{1}[1]{\color{darkgray}\bf 0.1 } & \scalebox{1}[1]{\color{darkgray}\bf 0.16} & \scalebox{1}[1]{\color{darkgray}\bf 0.11} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.05} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.05} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.8$} 
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.02} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.17} & \scalebox{1}[1]{\color{darkgray}\bf 0.09} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.9$} 
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.09} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.5$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.05} & \scalebox{1}[1]{\color{darkgray}\bf 0.15} & \scalebox{1}[1]{\color{darkgray}\bf 0.10 } & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.13} & \scalebox{1}[1]{\color{darkgray}\bf 0.02} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} 
\\
\cline{2-13}
&
    \multirow{10}{*}{\normalsize \begin{tabular}{c} $|V|$ \\ $=$ \\ 300 \end{tabular}}
&
      \multirow{2}{*}{\normalsize $\Phi=0.5$} 
         & \scalebox{1   }[1]{$\gamma=0.25$} 
         & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 0.99} & \scalebox{1.1}[1.1]{\bf 0.98} & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 0.69} & \scalebox{1.1}[1.1]{\bf 0.36} & \scalebox{1}[1]{\color{darkgray}\bf 0.16} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.16} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 0.98} & \scalebox{1.1}[1.1]{\bf 0.96} & \scalebox{1.1}[1.1]{\bf 1.00   } & \scalebox{1.1}[1.1]{\bf 0.69} & \scalebox{1.1}[1.1]{\bf 0.36} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.23} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.6$} 
         & \scalebox{1   }[1]{$\gamma=0.3$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.21} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} & \scalebox{1}[1]{\color{darkgray}\bf 0.12} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.14} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.03} & \scalebox{1}[1]{\color{darkgray}\bf 0.01} & \scalebox{1}[1]{\color{darkgray}\bf 0.15} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} & \scalebox{1}[1]{\color{darkgray}\bf 0.07} & \scalebox{1}[1]{\color{darkgray}\bf 0.09} & \scalebox{1}[1]{\color{darkgray}\bf 0.04} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.7$} 
         & \scalebox{1   }[1]{$\gamma=0.35$} 
         & \scalebox{1}[1]{\color{darkgray}\bf 0.06} & \scalebox{1}[1]{\color{darkgray}\bf 0.08} & \scalebox{1   }[1]{\color{darkgray}\bf 0.13} & \scalebox{1   }[1]{\color{darkgray}\bf 0.17} & \scalebox{1   }[1]{\color{darkgray}\bf 0.14} & \scalebox{1   }[1]{\color{darkgray}\bf 0.05} & \scalebox{1   }[1]{\color{darkgray}\bf 0.07} & \scalebox{1   }[1]{\color{darkgray}\bf 0.02} & \scalebox{1   }[1]{\color{darkgray}\bf 0.08} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1   }[1]{\color{darkgray}\bf 0.03} & \scalebox{1   }[1]{\color{darkgray}\bf 0.06} & \scalebox{1   }[1]{\color{darkgray}\bf 0.09} & \scalebox{1   }[1]{\color{darkgray}\bf 0.11} & \scalebox{1   }[1]{\color{darkgray}\bf 0.10 } & \scalebox{1   }[1]{\color{darkgray}\bf 0.08} & \scalebox{1   }[1]{\color{darkgray}\bf 0.02} & \scalebox{1   }[1]{\color{darkgray}\bf 0.02} & \scalebox{1   }[1]{\color{darkgray}\bf 0.05} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.8$} 
         & \scalebox{1   }[1]{$\gamma=0.4$} 
         & \scalebox{1   }[1]{\color{darkgray}\bf 0.04} & \scalebox{1   }[1]{\color{darkgray}\bf 0.09} & \scalebox{1   }[1]{\color{darkgray}\bf 0.12} & \scalebox{1   }[1]{\color{darkgray}\bf 0.14} & \scalebox{1   }[1]{\color{darkgray}\bf 0.12} & \scalebox{1   }[1]{\color{darkgray}\bf 0.11} & \scalebox{1   }[1]{\color{darkgray}\bf 0.04} & \scalebox{1   }[1]{\color{darkgray}\bf 0.05} & \scalebox{1   }[1]{\color{darkgray}\bf 0.08} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1   }[1]{\color{darkgray}\bf 0.04} & \scalebox{1   }[1]{\color{darkgray}\bf 0.17} & \scalebox{1   }[1]{\color{darkgray}\bf 0.11} & \scalebox{1   }[1]{\color{darkgray}\bf 0.15} & \scalebox{1   }[1]{\color{darkgray}\bf 0.17} & \scalebox{1   }[1]{\color{darkgray}\bf 0.09} & \scalebox{1   }[1]{\color{darkgray}\bf 0.04} & \scalebox{1   }[1]{\color{darkgray}\bf 0.04} & \scalebox{1   }[1]{\color{darkgray}\bf 0.05} 
\\
\cline{3-13}
&
&
      \multirow{2}{*}{\normalsize $\Phi=0.9$} 
         & \scalebox{1   }[1]{$\gamma=0.45$} 
         & \scalebox{1   }[1]{\color{darkgray}\bf 0.05} & \scalebox{1   }[1]{\color{darkgray}\bf 0.08} & \scalebox{1   }[1]{\color{darkgray}\bf 0.11} & \scalebox{1   }[1]{\color{darkgray}\bf 0.18} & \scalebox{1   }[1]{\color{darkgray}\bf 0.14} & \scalebox{1   }[1]{\color{darkgray}\bf 0.02} & \scalebox{1   }[1]{\color{darkgray}\bf 0.03} & \scalebox{1   }[1]{\color{darkgray}\bf 0.04} & \scalebox{1   }[1]{\color{darkgray}\bf 0.07} 
\\
&
&
         & \scalebox{1   }[1]{$\gamma=0.5$} 
         & \scalebox{1   }[1]{\color{darkgray}\bf 0.05} & \scalebox{1   }[1]{\color{darkgray}\bf 0.07} & \scalebox{1   }[1]{\color{darkgray}\bf 0.10 } & \scalebox{1   }[1]{\color{darkgray}\bf 0.21} & \scalebox{1   }[1]{\color{darkgray}\bf 0.11} & \scalebox{1   }[1]{\color{darkgray}\bf 0.09} & \scalebox{1   }[1]{\color{darkgray}\bf 0.04} & \scalebox{1   }[1]{\color{darkgray}\bf 0.01} & \scalebox{1   }[1]{\color{darkgray}\bf 0.05} 
\\
\hline
\\
\end{tabular}
\setlength{\extrarowheight}{0ex}
}
%
\end{center}
%
\end{table}


%%% END of table for sharp increase of xi at E=0.75 for homogeneous in-arborescence networks
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



















































\vspace*{0.1in}
\noindent
{\bf Formal intuition}

\vspace*{0.1in}
\noindent
A formal intuition behind such a sharp decrease of $\xi$ can be provided as follows.

\begin{lemma}[see Section~\ref{g9proof-sec} of the appendix for a proof]\label{g9}
Fix $\gamma$, $\Phi$, $\I$, a homogeneous in-arborescence network $G$ and assume that
$\gamma\approx \nicefrac{\Phi}{2}$. Consider any node $v\in\vs$ with $\din(v)>1$, suppose that $v$ fails due to the initial shock.
Let $u$ be any node such that $u$ is a ``leaf node'' (\IE, $\din(u)=0$), and $(u,v)\in E$.
Then, as the total external asset $\E$ of the network is varied, 
there exists a threshold value $\E_{\tau}(u)$ such that 
%
\begin{itemize}
\item
if $\E<\E_{\tau}(u)$ then $u$ will become insolvent, but

\item
if $\E>\E_{\tau}(u)$ then 
$u$ will not become insolvent at any time $t\geq 1$, and the shock will not propagate any further through $u$. 
\end{itemize}
%
\end{lemma}











The next lemma provides a lower 
bound, using the degree distributions of the Bar\'{a}basi-Albert preferential-attachment model~\cite{BaAl99}, 
on the expected value of the number of leaves in a random in-arborescence network for which Lemma~\ref{g9} can be applied.

\begin{lemma}[see Section~\ref{g10proof-sec} of the appendix for a proof]
\label{g10}
Consider a random in-arborescence $G=(V,E)$ generated by the Bar\'{a}basi-Albert preferential-attachment algorithm~{\rm\cite{BaAl99}} as outlined in Section~\ref{topo} and let 
%
\[
\widehat{V}=\left\{\,u\in V \, \big| \, \big( \din(u)=0 \big) \, \wedge \, \big( \exists\, v \colon \big( \big( \din(v)>1 \big) \, \wedge \, \big( (u,v)\in E \big) \, \big) \, \big) \, \right\}
\]
%
Then, $\ex\left[\big|\widehat{V}\big|\right]\geq \dfrac{n}{8}-\dfrac{11}{8}$.
\end{lemma}












Let 
$\xi(\E)$ be the value of $\xi$ parameterized by $\E$ (keeping all other parameters unchanged), and let
%
\begin{align*}
\E_{\tau_{\min}} & = \min \left\{ \E_{\tau}(u) \,\big|\, \din(u)=0,\, (u,v)\in E \text{ and } \din(v)>1\right\}
\\
\displaybreak[0]
\E_{\tau_{\max}} & = \max \left\{ \E_{\tau}(u) \,\big|\, \din(u)=0,\, (u,v)\in E \text{ and } \din(v)>1\right\}
\end{align*}
%
It then follows that
%
\[
\ex\left[\xi\left(\E_{\tau_{\min}}\right)\right]
-
\ex\left[\xi\left(\E_{\tau_{\max}}\right)\right]
\geq 
\frac
{
\frac{n}{8}-\frac{11}{8}
}
{n}
\approx \frac{1}{8}
\]
%
and $\xi\left(\E\right)$ exhibits a sharp decrease around the range $\left[\E_{\tau_{\min}},\,\E_{\tau_{\max}}\right]$.
In practice, the extent of this decrease is expected to be much more than the pessimistic lower bound of $\nicefrac{1}{8}$, as
our simulation results clearly show.





%

\section{Concluding remarks}
\label{concl-sec}

In this paper, we have initiated a methodology for systematic investigation of the global stabilities of financial networks that arise in 
OTC derivatives market and elsewhere. Our results can be viewed as a much needed beginning of a systematic investigation of these issues, with future
research works concentrating on further improving the network model, the stability measure and parameter choices.

\section*{Acknowledgment}

This work partially supported by NSF grant IIS-1160995.



\begin{thebibliography}{99}
\bibitem{Ace2013}
{\sc Acemoglu D., Ozdaglar A. \& Tahbaz-Salehi A.} (2013). Systemic risk and stability in financial networks. working paper.

\bibitem{AG08}
{\sc Allen F. \& Babus A.} (2009). Networks in Finance, 
in: Network-based Strategies and Competencies, Kleindorfer P., Wind J. (Eds.), Wharton School Publishing, 367-382.

\bibitem{AG2000}
{\sc Allen F. \& Gale D.} (2000). Financial Contagion. {\em Journal of Political Economy}, \textbf{108} (1), 1--33.

\bibitem{AS90}
{\sc Alon N. \& Spencer J. H.} (1992). The Probabilistic Method. John Wiley \& Sons, Inc. 

\bibitem{ACM11}
{\sc Amini H., Cont R. \& Minca A.} (2011). Resilience to contagion in financial networks, arXiv:1112.5687v1.

\bibitem{B07}
{\sc Babus A.} (2007a).
The Formation of Financial Networks,
Tinbergen Institute Discussion Paper No. 2006-093/2; FEEM Working Paper No. 69.2007.

\bibitem{A05}
{\sc Babus A.} (2007b). Contagion Risk in Financial Networks, in: Financial Development, Integration and Stability, 
Liebscher K., Christl J., Mooslechner P., Ritzberger-Grunwald D. (Eds.), Edward Elgar Pub, 423--440.

\bibitem{BaAl99}
{\sc Bar\'{a}basi A.-L. \& Albert R.} (1999). Emergence of Scaling in Random Networks. {\em Science}, \textbf{286}, 509--512.

\bibitem{arxiv}
{\sc Berman P., DasGupta B., Kaligounder L. \& Karpinski M.} (2013). On Systemic Stability of Banking Networks, {\em Algorithmica}, in press.

\bibitem{bolo}
{\sc Bollob\'{a}s B.} (2001). Random Graphs. Cambridge University Press.

\bibitem{Bo03}
{\sc Bollob\'{a}s B., Borgs C., Chayes T. \& Riordan O.} (2003). Directed scale-free graphs, 
in: $14\tx$ ACM-SIAM Symposium on Discrete Algorithms, 
Society for Industrial and Applied Mathematics, Philadelphia, PA, 
132-139.

\bibitem{BE98}
{\sc Borodin A. \& El-Yaniv R.} (1998). Online Computation and Competitive Analysis, Cambridge University Press.

\bibitem{borodin}
{\sc Borodin A., Filmus Y. \& Oren J.} (2010).
Threshold models for competitive influence in social networks,
$6\tx$ international conference on Internet and network economics, 
Springer-Verlag Berlin, Heidelberg,  
539--550.

\bibitem{C09}
{\sc Calabria M. A.} (2009). Did Deregulation Cause the Financial Crisis?, Cato Institute.

\bibitem{CNSW00}
{\sc Callaway D. S., Newman M. E. J., Strogatz S. H. \& Watts D. J.} (2000). Network robustness and fragility: percolation on random graphs.
{\em Physical Review Letters}, \textbf{85}, 5468--5471.

\bibitem{FN09}
{\sc Castiglionesi F. \& Navarro B.} (2007).
Optimal Fragile Financial Networks.
Tilburg University Discussion Paper no. 2007-100 (Tilburg, The Netherlands: Tilburg University).

\bibitem{Chen08}
{\sc Chen N.} (2008). On the approximability of influence in social networks, in:  
$19\tx$ ACM-SIAM Symposium on Discrete Algorithms, 
Society for Industrial and Applied Mathematics, Philadelphia, PA, 
1029--1037.

\bibitem{CWY09}
{\sc Chen W., Wang Y. \& Yang S.} (2009). Efficient influence maximization in social networks, in: 
$15\tx$ ACM SIGKDD international conference on Knowledge discovery and data mining, 
Association for Computing Machinery, New York, 
199--208.

\bibitem{coelho08}
{\sc Coelho F. C., Cruz O. G. \& Code�o C. T.} (2008).
Epigrass: a tool to study disease spread in complex networks.
{\em Source Code for Biology and Medicine}, \textbf{3} (3), 2008.

\bibitem{C10}
{\sc Cont R.} (2010). Credit default swaps and financial stability. {\em Finacial Stability Review (Banque de France)}, \textbf{14}, 35--43.

\bibitem{CMS10}
{\sc Cont R., Moussa A. \& Santos E. B.} (2010). Network Structure and Systemic Risk in Banking Systems. Working paper.

\bibitem{CD09}
{\sc Corbo J. \& Demange G.} (2010). in: $3^{\mathrm{rd}}$ Financial Risks International Forum, Paris, France.

\bibitem{D04}
{\sc Dasgupta B.} (2004).
Capital Accumulation in the Presence of Informal Credit Contracts: Does the Incentive Mechanism Work Better than Credit Rationing Under Asymmetric Information?,
Working papers 2004-32, University of Connecticut, Department of Economics.

\bibitem{DP83}
{\sc Diamond D. W. \& Dybvig P. H.} (1983). Bank runs, deposit insurance and liquidity. {\em Journal of Political Economy}, \textbf{91}, 401--419.

\bibitem{E04}
{\sc Eboli M.} (2004). Systemic Risk in Financial Network: a Graph Theoretical Approach. 
Mimeo, Univ. di Chieti, Pescara.

\bibitem{E2013}
{\sc Elliott M., Golub B. \& Jackson M. O.} (2013). Financial networks and contagion. Working paper.

\bibitem{ET08}
{\sc Ekelund R. \& Thornton M.} (2008). More Awful Truths About Republicans. Ludwig von Mises Institute. 

\bibitem{eubank05}
{\sc Eubank S.} (2005).  
Network based models of infectious disease spread.
{\em Japanese Journal of Infectious Diseases}, \textbf{58}, S19-S13.

\bibitem{eubank04}
{\sc Eubank S., Guclu H., Kumar V. S. A., Marathe M. V., Srinivasan A., Toroczkai Z. \& Wang N.} (2004).
Modeling Disease Outbreaks in Realistic Urban Social Networks.
{\em Nature}, \textbf{429}, 180--183.

\bibitem{F33}
{\sc Fisher I.} (1933). The Debt-Deflation Theory of Great Depressions. {\em Econometrica}, \textbf{1}, 337--357.

\bibitem{XBJ2000}
{\sc Freixas X., Parigi B. M. \& Rochet J.-C.} (2000). Systemic risk, interbank relations, and liquidity provision by the central bank.
{\em Journal of Money, Credit and Banking}, \textbf{32} (3), 611--638.

\bibitem{F03}
{\sc Furfine C. H.} (2003). Interbank exposures: Quantifying the risk of contagion. {\em Journal of Money, Credit and Banking}, \textbf{35} (1), 111--128.

\bibitem{GK08}
{\sc Gai P. \& Kapadia S.} (2010). Contagion in financial networks. {\em Proc. R. Soc. A}, \textbf{466} (2120), 2401--2423.

\bibitem{H09}
{\sc Haldane A.} (2009). Why Banks Failed the Stress Test.
speech given at the Marcus-Evans Conference on Stress-Testing, 9-10 February 2009 (available at \url{http://www.bankofengland.co.uk/publications/speeches/2009/speech374.pdf}).

\bibitem{HM11}
{\sc Haldane A. G. \& May R. M.} (2011). Systemic risk in banking ecosystems. {\em Nature}, \textbf{469}, 351--355.

\bibitem{HK00}
{\sc Hann J. \& Kamber M.} (2000). Data Mining: Concepts and Techniques. Morgan Kaufman Publishers.

\bibitem{AW12}
{\sc H\"{u}bsch A. \& Walther U.} (2012). The impact of network inhomogeneities on contagion and system stability, CPQF Working Paper 
Series, No. 32, Frankfurt School of Finance \& Management.

\bibitem{CM09}
{\sc Iazzetta C. \& Manna M.} (2009).
The Topology of the Interbank Market Developements in Italy Since 1990,
Bank of Italy Temi di Discussione (Working Paper) No. 711.

\bibitem{IP06}
{\sc Iyer R. \& Peydro J. L.} (2010). Interbank Contagion at Work: Evidence from a Natural Experiment. {\em Review of Financial Studies}, \textbf{24} (4), 1337--1377.

\bibitem{jones}
{\sc Jones C. M. \& Zhigljavsky A. A.} (2004). Approximating the negative moments of the Poisson distribution.
{\em Statistics \& Probability Letters}, \textbf{66} (2), 171--181.

\bibitem{kempe1}
{\sc Kempe D., Kleinberg J. \& Tardos E.} (2003).
Maximizing the spread of influence through a social network,
$9\tx$ ACM SIGKDD international conference on Knowledge discovery and data mining, 
Association for Computing Machinery, New York, 
137--146.

\bibitem{K36}
{\sc Keynes J. M.} (1936). The General Theory of Employment, Interest, and Money. New York: Harcourt, Brace and Company.

\bibitem{PYR09}
{\sc Kleindorfer P. R., Wind Y. \& Gunther R. E.} (2009). The Network Challenge: Strategy, Profit and Risk in an Interlinked World. Pearson Prentice Hall.

\bibitem{Knuth}
{\sc Knuth D. E.} (1997). The Art of Computer Programming (Fundamental Algorithms), Volume 1, Third Edition, Reading, Massachusetts: Addison-Wesley.

\bibitem{La13}
{\sc Ladley D.} (2013). Contagion and risk sharing on the inter-bank market, {\em Journal of Economics Dynamics \& Control}, \textbf{37}, 1384--1400.

\bibitem{RS98}
{\sc Lagunoff R. \& Schreft S.} (2001). A Model of Financial Fragility. {\em Journal of Economic Theory}, \textbf{99} (1-2), 220--264.

\bibitem{Lie2010}
{\sc Liedorp F. R., Medema L., Koetter M., Koning R. H. \& Lelyveld I. van} (2010).
Peer monitoring or contagion? Interbank market exposure and bank risk,
DNB working paper No. 248.

\bibitem{MGS09}
{\sc Markose S., Giansante S., Gatkowski M. \& Shaghaghi A. R.} (2009).
Too Interconnected To Fail: Financial Contagion and Systemic Risk In Network Model of CDS and Other Credit Enhancement Obligations of 
US Banks. Economics Discussion Papers 683, Department of Economics, University of Essex.

\bibitem{MA10}
{\sc May R. \& Arinaminpathy N.} (2010). Systemic risk: the dynamics of model banking systems. {\em J. R. Soc. Interface}, \textbf{7}, 823--838.

\bibitem{MMM11}
{\sc Minca A.} (2011). Mathematical modeling of default contagion. PhD thesis, Universite Paris VI (Pierre et Marie Curie).

\bibitem{MR13}
{\sc Minoiu C. \& Reyes J. A.} (2013). A Network Analysis of Global Banking: 1978-2010. {\em Journal of Financial Stability} (in press).

\bibitem{M77}
{\sc Minsky H.} (1977). A Theory of Systemic Fragility, in: Financial Crises: Institutions and Markets in a Fragile Environment, Altman E. I., Sametz A. W. (Eds.), Wiley.

\bibitem{M07}
{\sc Mistrulli P. E.} (2007). Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns. Bank of Italy Research.

\bibitem{M11}
{\sc Moussa A.} (2011). Thesis, Columbia University.

\bibitem{NYYA07}
{\sc Nier E., Yang J., Yorulmazer T. \& Alentorn A.} (2007). Network models and financial stability. {\em Journal of Economics Dynamics and Control}, \textbf{31}, 2033--2060.

\bibitem{OKK04}
{\sc Onnela K.-P., Kaski K. \& Kert\'{e}sz J.} (2004). Clustering and information in correlation based financial networks. {\em Eur. Phys. J. B}, \textbf{38}, 353--362.

\bibitem{rozanov}
{\sc Rozanov Y. A.} (1977). Probability Theory: A Concise Course. Dover Publications, Inc. 

\bibitem{A10}
{\sc Sachs A.} (2013). Completeness interconnectedness and distribution of interbank exposures - a parameterized analysis of the stability of financial networks.
{\em Quantitative Finance} (in press).

\bibitem{SR10}
{\sc Santos E. B. \& Cont R.} (2010). The Brazilian Interbank Network Structure and Systemic Risk. Working Papers Series 219, Central Bank of Brazil.

\bibitem{SOKK}
{\sc Saram\"{a}ki J., Onnela J.-P., Kert\'{e}sz J. \& Kaski K.} (2005).
Characterizing Motifs in Weighted Complex Networks, in: Science of Complex Networks, Mendes J. F. F. \EA (Eds.).

\bibitem{SA94}
{\sc Stauffer D. \& Aharony A.} (1994). Introduction to Percolation Theory, 2nd edition, CRC Press.

\bibitem{SM12}
{\sc Staum J. C. \& Liu M.} (2012). Systemic Risk Components in a Network Model of Contagion. Working paper,
Department of Industrial Engineering and Management Sciences, Northwestern University.

\bibitem{UW04}
{\sc Upper C. \& Worms A.} (2004). Estimating bilateral exposures in the german interbank market: Is there a danger of contagion?. {\em European Economic Review}, \textbf{48} (4), 827--849.

\bibitem{Z11}
{\sc Zawadowski A.} (2011). Entangled Financial Systems. Working paper, Boston University School of Management.
\end{thebibliography}



\appendix

\begin{center}
{\bf APPENDIX}
\end{center}


\section{Proof of Lemma~\ref{g1}}
\label{g1proof-sec}

We will reuse the notations in Definition~\ref{defnet}.
Using Equation~\eqref{eq1}, for every edge $(u,v)\in E$, the amount of shock received by node $u$ at time $t=1$ is as follows:
%
\begin{itemize}
\item
If $G$ is homogeneous then 
%
\begin{eqnarray*}
\ex \left[ \Delta_{\,\mathrm{homo}}(u) \right] 
&
=
&
\frac
{
\min \left\{ \Phi \left( \din(v) - \dout(v) + \frac{\E}{n} \right) \,-\, \gamma \left( \din(v) + \frac{\E}{n} \right), \, \din(v) \right\}
}
{
\din(v)
}
\\
&
=
&
\min \left\{
\big( \Phi - \gamma \big) + 
%%
\frac { \frac{\E}{n} (\Phi - \gamma) \,-\, \Phi \, \dout(v) } { \din(v) }
, \, 
1
\right\}
\end{eqnarray*}
%














\item
If $G$ is $(\alpha,\beta)$-heterogeneous, then 
$\sigma_v=\frac{\beta}{\alpha}$ 
and, using linearity of expectation, we get
%%%%%%%%%%%
%%%%%%%%%%%
%%%%%%%%%%%
\begin{align*}
\ex\left[b_v\right]
&
= 
\ex
\left[
\sum_{(u,v)\in \widetilde{E}}
%%%
\left(
\,
\alpha\,\frac {\beta \I} {\alpha\,|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
\\
\displaybreak[0]
&
=
\din(v) \, 
\ex
\left[
%%%
\left(
\,
\beta\,\frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
\\
\displaybreak[0]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&
\\
\displaybreak[0]
\ex\left[b_v-\iota_v\right] 
&
=
\ex
\left[
\sum_{(u,v)\in \widetilde{E}}
%%%
\left(
\,
\alpha\,\frac {\beta \I} {\alpha\,|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\,-\,
\sum_{(v,u)\in \widetilde{E}}
%%%
\left(
\,
\alpha\,\frac {\beta \I} {\alpha\,|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
\\
\displaybreak[0]
%%%%%%%%
&
=
\sum_{(u,v)\in \widetilde{E}}
%%%
\ex
\left[
\left(
\,
\beta\, \frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
\,-\,
\sum_{(v,u)\in \widetilde{E}}
%%%
\ex
\left[
\left(
\,
\beta \, \frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
\\
\displaybreak[0]
&
=
\big(\,\din(v) - \dout(v) \, \big)
\,
\ex
\left[
\left(
\,
\beta \, \frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
\\
\displaybreak[0]
&
\\
\displaybreak[0]
%
\ex \left[ \Delta_{\,\mathrm{hetero}}(u) \right] 
&
= 
\ex \left[
\frac
{
\min \left\{ \Phi \left( b_v - \iota_v + \sigma_v \, \E \right) - \gamma \left( b_v + \sigma_v\,\E \right), \, b_v \right\}
}
{
\din(v)
}
\right]
\\
\displaybreak[0]
&
=
\min 
\left\{
\ex \left[
\frac
{
 \Phi \left( b_v - \iota_v + \sigma_v \, \E \right) - \gamma \left( b_v + \sigma_v\,\E \right)
}
{
\din(v)
}
\right]
,
\,
\ex
\left[
\frac{b_v}{\din(v)}
\right]
\right\}
\\
\displaybreak[0]
&
=
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\min 
\left\{
\frac{\Phi}{\din(v)} \, \ex \left[ b_v - \iota_v \right]
\,+\,
\frac{\Phi\,\sigma_v\,\E}{\din(v)}
\,-\,
\frac{\gamma}{\din(v)} \, \ex \left[ b_v \right]
\,-\,
\frac{\gamma\,\sigma_v\,\E}{\din(v)}
,
\,\,
\frac{1}{\din(v)}
\,
\ex
\left[
b_v
\right]
\right\}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\displaybreak[0]
&
\textstyle
=
\,
\min 
\left\{
\frac{\Phi}{\din(v)} \, 
%%%%%%%%%%
\big(\,\din(v) - \dout(v) \, \big)
\,
\ex
\left[
\left(
\,
\beta\,\frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
%%%%%%%%%%
\,+\,
\frac{\Phi\,\sigma_v\,\E}{\din(v)}
\right.
\\
\displaybreak[0]
&
\hspace*{0.7in}
\textstyle
\,-\,
\frac{\gamma}{\din(v)} \, 
%%%%%%%
\din(v) \, 
\ex
\left[
%%%
\left(
\,
\beta \,\frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
%%%%%%%
\,-\,
\frac{\gamma\,\sigma_v\,\E}{\din(v)}
,
\\
\displaybreak[0]
&
\hspace*{1.2in}
\textstyle
\left.
\ex
\left[
%%%
\left(
\,
\beta\,\frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
%%%%%%%%%%%%%%%%%%
\,
\right\}
\\
%%%%%%%%%%%%%%%%%%
\displaybreak[0]
&
\textstyle
=
\min 
\left\{
\frac{  \Phi \, \big( \din(v) - \dout(v)  \big) - \gamma\,\din(v)}{\din(v)}
\,
\ex
\left[
\left(
\,
\beta\,\frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
\,+\,
\frac{\big(\Phi - \gamma \big)\,\sigma_v\,\E}{\din(v)}
,
\right.
\\
\displaybreak[0]
&
\hspace*{0.7in}
\textstyle
\left.
\ex
\left[
%%%
\left(
\,
\beta\,\frac {\I} {|\widetilde{E}|}
+
\big(1-\alpha\big) \, 
\frac {\big(1-\beta\big)\,\I} {|E|-\alpha\,|\widetilde{E}|}
\,
\right)
\right]
\,
\right\}
\\
%%%%%%%%%%%%%%%%%%
\displaybreak[0]
&
\textstyle
\geq
\min 
\left\{
\frac{ \Phi \, \big( \din(v) - \dout(v)  \big) - \gamma\,\din(v) }{\din(v)}
\,
\beta
\,
\ex
\left[
\frac {\I} {|\widetilde{E}|}
\right]
\,+\,
\frac{\big(\Phi - \gamma\big)\,\sigma_v\,\E}{\din(v)}
,
\,\,
\beta
\,
\ex
\left[
%%%
\frac {\I} {|\widetilde{E}|}
\right]
\right\}
\\
%%%%%%%%%%%%%%%%%%
\displaybreak[0]
&
\textstyle
\geq
\min 
\left\{
\,
\left(
\frac{  \Phi \, \big( \din(v) - \dout(v)  \big) -          \gamma\,\din(v)  }{\din(v)}
\right)
\,
\left(
\frac{\beta}{\alpha}
\right)
\,+\,
\left(
\frac{\beta}{\alpha}
\right)
\,
\left(
\frac{\big(\Phi - \gamma \big)\,\E}{\din(v)}
\right)
,
\,
\frac{\beta}{\alpha}
\,
\right\}
\\
\displaybreak[0]
&
\hspace*{0.7in}
\textstyle
\text{\small since } \ex \left[ \frac {\I} {|\widetilde{E}|} \right] = \ex \left[ \frac {|E|} {|\widetilde{E}|} \right] = \alpha
\\
\displaybreak[0]
&
\geq
\frac{\beta}{\alpha}
\,
\min 
\left\{
\,
\big(\Phi - \gamma \big)
+
\frac
{
\big(\Phi - \gamma \big)\,\E
-
\Phi\,\dout(v)
}
{
\din(v)
}
,
\,\,
1
\,
\right\}
\\
\displaybreak[0]
&
\geq 
\frac{\beta}{\alpha}
\,
\ex \left[ \Delta_{\,\mathrm{homo}}(u) \right] 
\end{align*}
%
\end{itemize}
%

\section{Proof of Lemma~\ref{bb1}}
\label{bb1proof-sec}

Using standard probabilistic calculations, we get
%
\[
\ex\left[\frac{1}{\din(v)} \, \Big| \, \din(v)>0 \right]
=
\sum_{k=1}^{n-1} \frac{1}{k} \, \Pr\left[ \din(v)=k\right] 
=
C\,\sum_{k=1}^{n-1} k^{-4}
\approx 
C\,\zeta(4)
\approx
\frac{\pi^2}{15}\,\dave
\]
%
\begin{multline*}
\Var\left[\din(v)\right] =
\ex\left[\,\left(\din(v)\right)^2\right] - \left(\ex\left[\din(v)\right]\right)^2
=
\sum_{k=1}^{n-1} k^2 \left( C k^{-3} \right) - \left( \dave \right)^2
\\
= C \sum_{k=1}^{n-1} \frac{1}{k} - \left( \dave \right)^2
\approx 
\frac{6\,\dave}{\pi^2} \,\ln n - \left( \dave \right)^2
\approx 
\frac{6\,\dave}{\pi^2} \,\ln n 
\end{multline*}
%



\section{Proof of Lemma~\ref{c1het-lemma}}
\label{c1het-lemmaproof-sec}

Let $\cD=
\sum\limits_{v \in \widetilde{V}} \din(v)
+
\sum\limits_{v \in \widetilde{V}} \dout(v)
$.
By linearity of expectation, we have 
%
\[
\ex \left[
\cD
\right]
=
2\,
\sum_{v \in \widetilde{V}} \ex \left[\din(v)\right]
=
2\,\alpha\,n\,\dave
\]
%
and similarly, since $\din(v)$ is independent of any other $\din(u)$ for $u\neq v$, we have 
%
\[
\Var \left[
\cD
\right]
=
2\,
\sum_{v \in \widetilde{V}} \Var \left[\din(v)\right]
\approx 
\frac{12\,\dave}{\pi^2} \,\alpha\,n\,\ln n 
\]
%
Thus, via Chebyschev's inequality~\cite[page 37]{AS90}, for any positive $\lambda$ we have 
%
\[
\textstyle
\Pr \left[
\,
\left|\,
\cD
\,
-
\,
\ex \left[
\cD
\right]
\,\right|
\geq 
\lambda\,
\sqrt{
\Var \left[
\cD
\right]
}
\,
\right]
\leq
\frac{1}{\lambda^2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\,\equiv \,
\Pr \left[
\,
\left|\,
\cD
\,
-
\,
2\,\alpha\,n\,\dave
\,\right|
\gtrapprox
\lambda\,
\sqrt{
\frac{12\,\dave}{\pi^2} \,\alpha\,n\,\ln n 
}
\,
\right]
\leq
\frac{1}{\lambda^2}
\]
%
Setting $\lambda=
\sqrt{
\frac{\pi^2\,\ln n}{12\,\alpha}
}
$ 
gives 
%
$
\Pr \left[
\,
\left|\,
\cD
\,
-
\,
2\,\alpha\,n\,\dave
\,\right|
\gtrapprox
\sqrt{n\, \dave}\,\ln n
\,
\right]
\leq
\dfrac {12\,\alpha} {\pi^2\,\ln n}
$
%
and thus {\tt w.h.p.}  
$\,\,
\cD \approx 
2\,\alpha\,n\,\dave
$.
Since 
%
$
\frac{\cD}{2}
\leq
|\,\widetilde{E}\,|
\leq 
\cD
$, 
%
it now follows that
%
\begin{eqnarray*}
\alpha\,n\,\dave
\leq
&
\ex\left[ | \, \widetilde{E} \, | \right]
&
\leq 
2\,\alpha\,n\,\dave
\\
\mbox{\tt w.h.p.}
\,\,\, \,\,\,
\alpha\,n\,\dave
\leq
&
|\,\widetilde{E}\,|
&
\leq 
2\,\alpha\,n\,\dave
\end{eqnarray*}
%
Also, note that
%
$
\Pr\left[ (u,v)\in \widetilde{E} \right]
=
\Pr\left[v\in\widetilde{V}\right]=\alpha
$.
%
For notational convenience, let $\widetilde{E}_1$ be a random subset of $\alpha|\widetilde{E}|$ of edges from the edges in $\widetilde{E}$
as used in Definition~\ref{defnet}.
This implies that 
%
\begin{align*}
&
\begin{aligned}
\ex\left[c_1^{\mathrm{hetero}}\right]  
&
=
\Pr\left[ (u,v)\in \widetilde{E}_1 \right] \,\left( \frac{\beta\,\I}{\alpha\,|\,\widetilde{E}\,|} \right)
+ 
\left( 1 - \Pr\left[ (u,v)\in \widetilde{E}_1 \right]\, \right) \, \frac{\I - \beta \,\I}{|E| - \alpha \, |\,\widetilde{E}\,|}
\\
&
=
\alpha \, \Pr\left[ (u,v)\in \widetilde{E} \right] \,\left( \frac{\beta\,\I}{\alpha\,|\,\widetilde{E}\,|} \right)
+ 
\left( 1 - \alpha\,\Pr\left[ (u,v)\in \widetilde{E} \right]\, \right) \, \frac{\I - \beta \,\I}{|E| - \alpha \, |\,\widetilde{E}\,|}
\\
&
=
\alpha^2 \, \left( \frac{\beta\,\I}{\alpha\,|\,\widetilde{E}\,|} \right)
+
\left( 1 - \alpha^2 \,\right) \, \frac{\I - \beta \,\I}{|E| - \alpha \, |\,\widetilde{E}\,|}
\end{aligned}
\\
\displaybreak[0]
%
\Rightarrow
\,\,
&
\mbox{\tt w.h.p. } 
\,
\alpha^2 \, \frac{\beta\,n\,\dave}{2\, \alpha\,n\,\dave } + \left (1-\alpha^2 \right)\,\frac{(1-\beta)\,n\,\dave}{n\,\dave - \alpha\,n\,\dave}
\\
\displaybreak[0]
%
&
\hspace*{1.7in}
\leq 
\ex\left[c_1^{\mathrm{hetero}}\right]  
\leq 
\alpha^2 \, \frac{\beta\,n\,\dave}{\alpha\,n\,\dave } + \left(1-\alpha^2\right)\,\frac{(1-\beta)\,n\,\dave}{n\,\dave - 2\,\alpha\,n\,\dave}
\\
\displaybreak[0]
%
\equiv \,\, 
&
\mbox{\tt w.h.p. } 
\frac{\alpha\,\beta}{2} +
\left( 1 + \alpha \right) \, ( 1 - \beta ) 
\leq 
\ex\left[c_1^{\mathrm{hetero}}\right]  
\leq 
\alpha\,\beta +
\frac{\left( 1 - \alpha^2 \right) \, ( 1 - \beta ) } { 1 - 2\alpha }
\\
\displaybreak[0]
%
\equiv \,\, 
&
\mbox{\tt w.h.p. } 
1 + \alpha - \beta - \frac{\alpha\,\beta}{2}
\leq 
\ex\left[c_1^{\mathrm{hetero}}\right]  
\leq 
\frac{1 + \alpha\,\beta - \alpha^2 - \beta - \alpha^2\,\beta}{1-2\,\alpha}
\end{align*}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Proof of Lemma~\ref{bb3}}
\label{bb3proof-sec}

$\ex\left[\frac{1}{\din(v)}\right] = \sum\limits_{k=1}^{n-1} \frac{1}{k} \, \Pr\left[ \din(v)=k\right]
= \sum\limits_{k=1}^{n-1 } \frac{1}{k} \, \e^{-\dave} \, \frac{(\dave)^k}{k!}$. 
%
It is easy to see that extending the finite series to an infinite series does not change the asymptotic value of the series since 
%
\[
\begin{array}{r l l}
&
\sum\limits_{k=1}^{\infty} \dfrac{1}{k} \, \e^{-\dave} \, \dfrac{(\dave)^k}{k!}
\,-\,
\sum\limits_{k=1}^{n-1} \dfrac{1}{k} \, \e^{-\dave} \, \dfrac{(\dave)^k}{k!}
&
\\
=
&
\sum\limits_{k=n}^{\infty} \frac{1}{k} \, \e^{-\dave} \, \dfrac{(\dave)^k}{k!}
&
\\
\leq 
&
\frac{\e^{-\dave}}{n} \, \sum_{k=n}^{\infty} \dfrac{(\dave)^k}{k!}
&
\\
[0.1in]
\leq
&
\left( \dfrac{\e^{-\dave}}{n} \right) \, \left( \dfrac{(\dave)^n}{n!} \right) \, \left( \max\limits_{0\leq x\leq \dave} \left\{ \e^{x} \right\} \right)
&
\mbox{\begin{tabular}{l} using the Lagrange remainder term \\ for the Maclaurin series expansion of $\e^{\dave}$ \end{tabular}}
\\
[0.1in]
=
&
\left( \dfrac{\e^{-\dave}}{n} \right) \, \left( \dfrac{(\dave)^n}{n!} \right) \, \e^{\dave}
&
\\
[0.1in]
=
&
\dfrac{(\dave)^n}{n \, (n!) }
&
\end{array}
\]
%
and 
$\lim\limits_{n\to\infty} \frac{(\dave)^n}{n \, (n!) }$ because $\dave$ is a constant independent of $n$.
Thus, we can conclude that 
$\sum\limits_{k=1}^{\infty} \frac{1}{k} \, \e^{-\dave} \, \frac{(\dave)^k}{k!} \approx \sum\limits_{k=1}^{n-1} \frac{1}{k} \, \e^{-\dave} \, \frac{(\dave)^k}{k!}$.
%
It now follows that
%
\begin{multline*}
\dfrac{\partial }{\partial\, d}
\ex\left[\frac{1}{\din(v)} \, \big| \, \dave=d\right]
\approx
\dfrac{\partial }{\partial\, d}
\sum\limits_{k=1}^{\infty} \frac{1}{k} \, \e^{-d} \, \frac{d^k}{k!}
\\
=
\e^{-d} \, \sum\limits_{k=1}^{\infty} \frac{d^{k-1}}{k!}
=
\frac{\e^{-d}}{d} \, \sum\limits_{k=1}^{\infty} \frac{d^k}{k!}
=
\frac{\e^{-d}}{d} \, \left( \e^d - 1 \right)
=
\frac{1-\e^{-d}}{d}
\end{multline*}
%
This proves one of the claims in the lemma. To prove the other claim, 
using a well-known approximation on the first inverse moment of Poisson's distribution~\cite[page 173]{jones} we have 
%
\[
\left| \, 
\sum_{k=1}^{\infty} \, \frac{1}{k} \, \e^{-\dave} \, \frac{(\dave)^k}{k!}
\,-\,
\sum_{k=1}^{\lfloor 3\,\dave + 10 \rfloor } \, \frac{1}{k} \, \e^{-\dave} \, \frac{(\dave)^k}{k!}
\, \right| 
< 10^{-10}
\]
%
and therefore we obtain 
%
\[
\left| \, 
\sum_{k=1}^{n-1} \frac{1}{k} \, \e^{-\dave} \, \frac{(\dave)^k}{k!}
\,-\,
\sum_{k=1}^{\lfloor 3\,\dave + 10 \rfloor } \frac{1}{k} \, \e^{-\dave} \, \frac{(\dave)^k}{k!}
\, \right| 
\lessapprox 10^{-10}
\]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Proof of Lemma~\ref{bb4}}
\label{bb4proof-sec}

Let $\cD=
\sum_{v \in \widetilde{V}} \din(v)
+
\sum_{v \in \widetilde{V}} \dout(v)
$.
We can reuse the proof of Lemma~\ref{c1het-lemma} provided we show that 
$\ex \left[\cD \right]=2\,\alpha\,n\,\dave$ and 
{\tt w.h.p.}  $\,\,\cD \approx 2\,\alpha\,n\,\dave$.
%
By linearity of expectation, we have 
%
$
\ex \left[
\cD
\right]
=
2\,
\sum_{v \in \widetilde{V}} \ex \left[\din(v)\right]
=
2\,\alpha\,n\,\dave
$, 
%
and similarly
%
$
\Var \left[
\cD
\right]
\allowbreak
=
2\,
\sum_{v \in \widetilde{V}} \Var \left[\din(v)\right]
=
2\,\alpha\,n\,
\Big(1-\frac{\dave}{n-1} \Big)\,\dave
\approx 
2\,\alpha\,n\,\dave$.
%
Thus, via Chebyschev's inequality, for any positive $\lambda$ we have 
%
\[
\Pr \left[
\,
\left|\,
\cD
\,
-
\,
\ex \left[
\cD
\right]
\,\right|
\geq 
\lambda\,
\sqrt{
\Var \left[
\cD
\right]
}
\,
\right]
\leq
\frac{1}{\lambda^2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\,\equiv \,
\Pr \left[
\,
\left|\,
\cD
\,
-
\,
2\,\alpha\,n\,\dave
\,\right|
\gtrapprox
\lambda\,
\sqrt{
2\,\alpha\,n\,\dave
}
\,
\right]
\leq
\frac{1}{\lambda^2}
\]
%
Setting $\lambda=
\sqrt{
\frac{\ln n}{2\,\alpha}
}
$ 
gives 
%
\[
\Pr \left[
\,
\left|\,
\cD
\,
-
\,
2\,\alpha\,n\,\dave
\,\right|
\gtrapprox
\sqrt{n\, \dave\,\ln n}
\,
\right]
\leq
\dfrac {2\,\alpha} {\ln n}
\]
%
and thus {\tt w.h.p.}  
$\,\,
\cD \approx 
2\,\alpha\,n\,\dave
$.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%











\section{Proof of Lemma~\ref{g9}}
\label{g9proof-sec}

The amount of shock $\mu$ transmitted from $v$ to $u$ is given by 
%
\[
\mu=
\min 
\left\{
\left(\Phi-\gamma\right) \, \left( 1 + \frac{\E}{n\,\din(v)} \right)
+
\Phi \, \frac{\dout(v)}{\din(v)}
,\, 1
\right\}
\]
%
Since $G$ is an in-arborescence, $\dout(v)\leq 1$. First, consider the case of $\dout(v)=0$. In this case,
%
$
\mu
=
\min 
\left\{
\left(\Phi-\gamma\right) \, \left( 1 + \frac{\E}{n\,\din(v)} \right)
,\, 1
\right\}
$
%
and thus we have 
%
\[
c_u(1)=c_u(0) - \mu
=
\gamma \,
\frac{\E}{n}
\,-\,
\min 
\left\{
\left(\Phi-\gamma\right) \, \left( 1 + \frac{\E}{n\,\din(v)} \right)
,\, 1
\right\}
\]
%
Assuming $\gamma\approx \nicefrac{\Phi}{2}$, we have 
%
\begin{multline*}
c_u(1)
\approx
\gamma \, 
\frac{\E}{n}+\din(u)
\,-\,
\min 
\left\{
\gamma \, \left( 1 + \frac{\E}{n\,\din(v)} \right)
,\, 1
\right\}
\\
=
\min 
\left\{
\gamma \, \left(
\frac{\E}{n}
- 1 - \frac{\E}{n\,\din(v)}
\right)
,\,\,
\gamma \, 
\frac{\E}{n}
-1
\right\}
\end{multline*}
%
There are two cases to consider:
%
\begin{itemize}
\item
If
$
\gamma \, \left(
\frac{\E}{n}
- 1 - \frac{\E}{n\,\din(v)}
\right)
\geq 
\gamma \, 
\frac{\E}{n}
-1
$
then 
%
\[
c_u(1)
\approx
\gamma \, \left(
\dfrac{\E}{n}
- 1 - \dfrac{\E}{n\,\din(v)}
\right)
=
\gamma \, \left(
\frac{\E}{n} \,
%
\left(
1 - \frac{1}{\din(v)}
\right)
%
-1
%
\right)
\]
%
Thus, if  $\E> \E_{\tau_1}(u) = \frac{n}{ 1 - \frac{1}{\din(v)} }$ then $c_u(1)$ would be strictly positive, the node 
$u$ will not become insolvent at time $t=1$, but if 
$\E< \E_{\tau_1}(u)$ then $c_u(1)$ would be strictly negative and $u$ would fail.

\item
Otherwise,
%
$c_u(1) \approx \gamma \, \frac{\E}{n} -1$.
%
Thus, if  $\E > \E_{\tau_2}(u) = \frac{n}{ \E }$ then $c_u(1)$ would be strictly positive, the node $u$ will not become insolvent
at time $t=1$, but if 
$\E< \E_{\tau_1}(u)$ then $c_u(1)$ would be strictly negative and $u$ would fail.
\end{itemize}
%
A similar analysis may be carried out if $\dout(v)=1$ leading to {\em slightly} two different threshold values, say $\E_{\tau_3}(u)$ and $\E_{\tau_4}(u)$. 
Since $\dout(u)=1$, if $u$ does not become insolvent at time $t=1$ then it does not become insolvent for any $t>1$ as well.













\section{Proof of Lemma~\ref{g10}}
\label{g10proof-sec}

Let $r$ be the root node of $G$. Note that, for any node $u\in V\setminus \{r\}$, $\dout(u)=1$. Thus, using the results in~\cite{BaAl99}, it follows that for any 
node $u\in V\setminus \{r\}$, $\Pr\left[\din(u)=k-1\right]\propto \nicefrac{1}{k^{3}}$ and in particular 
$\Pr\left[\din(u)=1\right]\leq \nicefrac{1}{4}$.
For $j=0,2,\dots,n$, let $n_j$ be the number of nodes $u$ of $G$ with $\din(u)=j$. 
Thus, $n=\sum\limits_{j=0}^n n_j$, $|E|=n-1=\sum\limits_{j=1}^n j\,n_j$, and 
%
\begin{multline*}
\sum_{u\in V\setminus \{r\}} \Pr\left[\din(u)=1\right]
\leq
\ex\left[n_1\right]
\leq 
1+ \sum_{u\in V\setminus \{r\}} \Pr\left[\din(u)=1\right]
\\
\displaybreak[0]
\equiv\,
\frac{n-1}{4}
\leq
\ex\left[n_1\right]
\leq 
1+\frac{n-1}{4}
\,\equiv\,
\ex\left[n_1\right]
=
\frac{n-1}{4}+t \,\,\,\,\,\, \text{ for some } t\in[0,1]
\end{multline*}
%
Letting $n_{>1}=\sum\limits_{j=2}^n n_j$, we have 
%
\begin{align*}
&
\ex\left[n_0+n_{>1}\right]  = n - \ex\left[n_1\right] = \frac{3n+1}{4} - t 
\\
\displaybreak[0]
&
\\
\displaybreak[0]
&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ex\left[\sum_{j=1}^n j\,n_j\right]  =  n-1 
\,\equiv\,\, 
\ex\left[n_1\right]  + \ex\left[\sum_{j=2}^n j\,n_j\right]  =  n-1 
\\
\displaybreak[0]
&
\hspace*{0.5in}
\equiv\,\,
\ex\left[n_1\right]  + 2\,\ex\left[n_{>1}\right] \leq  n-1 
\,\Rightarrow\,\,
\ex\left[n_{>1}\right] \leq  \frac{n-1 - \frac{3n+1}{4} + t}{2} 
= \frac{n}{8} +\frac{4t-5}{8}
\\
\displaybreak[0]
&
\\
\displaybreak[0]
&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ex\left[n_0\right]=n-\ex\left[n_1\right]-\ex\left[n_{>1}\right]
\geq
n- \left( \frac{n-1}{4}+t \right) - \left( \frac{n}{8} +\frac{4t-5}{8} \right)
=
\frac{n}{8} + \frac{7}{8} - \frac{3\,t}{2}
\end{align*}
%
and hence we can bound $\ex\left[\big|\widehat{V}\big|\right]$ as 
%
\begin{multline*}
\ex\left[\big|\widehat{V}\big|\right]
= \ex \left[ n_0 \right] - 
\ex \left[ \, \left| \, \left\{\,u\in V \, \big| \, \big( \din(u)=0 \big) \, \wedge \, \big( \exists\, v \colon \big( \big( \din(v)=1 \big) \, \wedge \, \big( (u,v)\in E \big) \, \big) \, \big) \, \right\} \, \right| \, \right]
\\
\displaybreak[0]
\geq 
\ex \left[ n_0 \right] - \ex \left[ n_1 \right] 
\geq
\left( \frac{n}{8} + \frac{7}{8} - \frac{3\,t}{2} \right)
-
\left( \frac{n-1}{4}+t \right)
=
\frac{n}{8} + \frac{9}{8} - \frac{5\,t}{2}
\geq 
\frac{n}{8} - \frac{11}{8} 
\end{multline*}
%














%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Supplemental information follows
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage

\newpage

\renewcommand{\thetable}{S\arabic{table}}
\setcounter{table}{0}

\begin{table}
\hspace*{-0.7in}
\begin{tabular}{c}
\toprule
\\
\\
\\
\bf {\Huge Supplementary documents follow}
\\
\\
\\
\bf {\Huge Supplementary Table~\ref{table7}---Table~\ref{supp4-table7}}
\\
\\
\\
\bf {\Huge Supplementary color figures {\sc Fig}.~\ref{newfig1}---{\sc Fig}.~\ref{supp-newfig5-full}}
\\
\\
\\
\bottomrule
\end{tabular}
\end{table}

\clearpage
\newpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% coordinated shock
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Another table for analysis of residual instability of homogeneous versus heterogeneous networks

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under idiosyncratic shocks. 
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.}
%
\label{table7}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf idiosyncratic shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.5,\gamma=0.45$}
&
\multicolumn{3}{c}{$\Phi=0.5,\gamma=0.40$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 76\%  & \bf 78\%  &  \bf 82\% & \bf 26\% \bf & \bf 58\%  & \bf 75\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 99\%  & \bf 100\%  &  \bf 100\% & \bf 43\% \bf & \bf 84\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 42\%  & \bf 100\%  &  \bf 100\% & \bf 23\% \bf & \bf 70\%  & \bf 88\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 2\%  &  15\% & 0\% \bf & 1\%  & 10\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 2\%  &  16\% & 0\% \bf & 1\%  & 8\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 10\%  &  21\% & 2\% \bf & 7\%  & 14\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 6\%  &  22\% & 0\% \bf & 2\%  & 14\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
8\%  & 19\%  &  34\% & 4\% \bf & 12\%  & 21\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 2\%  &  12\% & 0\% \bf & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
7\%  & 14\%  &  22\% & 4\% \bf & 9\%  & 18\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
8\%  & 18\%  &  30\% & 6\% \bf & 10\%  & 20\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  19\% & 0\% \bf & 3\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
8\%  & 12\%  &  24\% & 4\% \bf & 7\%  & 18\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 76\%  & \bf 78\%  &  \bf 81\% & \bf 32\% \bf & \bf 62\%  & \bf 81\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 66\%  & \bf 100\%  &  \bf 100\% & \bf 26\% \bf & \bf 74\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 29\%  & \bf 72\%  &  \bf 100\% & \bf 19\% \bf & \bf 53\%  & \bf 88\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 88\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 1\%  &  12\% & 0\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 0\%  &  15\% & 0\% & 1\%  & 10\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
6\%  & 7\%  &  16\% & 6\% & 6\%  & 10\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 6\%  &  23\% & 0\% & 0\%  & 16\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
8\%  & 16\%  &  30\% & 6\% & 12\%  & 19\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 1\%  &  11\% & 0\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
6\%  & 10\%  &  18\% & 0\% & 7\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 12\%  &  22\% & 6\% & 8\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 2\%  &  18\% & 0\% & 0\%  & 16\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
5\%  & 9\%  &  18\% & 2\% & 6\%  & 16\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 76\%  & \bf 78\%  &  \bf 81\% & \bf 36\% \bf & \bf 67\%  & \bf 81\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 76\%  & \bf 100\%  &  \bf 100\% & \bf 22\% \bf & \bf 73\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 26\%  & \bf 52\%  &  \bf 100\% & \bf 20\% \bf & \bf 42\%  & \bf 88\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 87\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 1\%  &  12\% & 0\% & 1\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 2\%  &  16\% & 0\% & 0\%  & 5\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
0\%  & 6\%  &  12\% & 0\% & 2\%  & 6\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  24\% & 0\% & 1\%  & 16\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 16\%  &  28\% & 6\% & 9\%  & 19\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 1\%  &  11\% & 0\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
6\%  & 8\%  &  16\% & 0\% & 2\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
6\%  & 8\%  &  17\% & 6\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  16\% & 0\% & 0\%  & 16\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
2\%  & 6\%  &  16\% & 2\% & 5\%  & 16\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
%
\end{table}

\clearpage

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks.
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.}
%
\label{supp1-table6}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf coordinated shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.6,\gamma=0.55$}
&
\multicolumn{3}{c}{$\Phi=0.6,\gamma=0.50$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 2\% \bf & \bf 69\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 97\%  & \bf 100\%  &  \bf 100\% & \bf 64\% \bf & \bf 95\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 56\%  & \bf 96\%  &  \bf 100\% & \bf 44\% \bf & \bf 87\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  1\% & 0\% \bf & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 0\%  &  5\% & 0\% \bf & 0\%  & 1\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
9\%  & 11\%  &  14\% & 5\% \bf & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
5\%  & 9\%  &  19\% & 0\% \bf & 3\%  & 8\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
22\%  & 28\%  &  41\% & 10\% \bf & 15\%  & 17\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% \bf & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
5\%  & 7\%  &  20\% & 3\% \bf & 7\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
11\%  & 14\%  &  26\% & 7\% \bf & 7\%  & 19\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
2\%  & 8\%  &  23\% & 1\% \bf & 3\%  & 18\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 15\%  &  26\% & 7\% \bf & 8\%  & 18\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 23\% \bf & \bf 84\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 85\%  & \bf 100\%  &  \bf 100\% & \bf 47\% \bf & \bf 86\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 37\%  & \bf 75\%  &  \bf 100\% & \bf 35\% \bf & \bf 71\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 96\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 0\%  & 3\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  9\% & 7\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  9\% & 0\% & 0\%  & 5\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
10\%  & 15\%  &  21\% & 7\% & 7\%  & 11\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 7\%  &  17\% & 0\% & 5\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  19\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 3\%  &  15\% & 0\% & 1\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 9\%  &  18\% & 7\% & 7\%  & 17\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 79\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 93\%  & \bf 100\%  &  \bf 100\% & \bf 48\% \bf & \bf 85\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 28\%  & \bf 56\%  &  \bf 97\% & \bf 28\% \bf & \bf 56\%  & \bf 97\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 93\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 0\%  & 3\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  7\% & 3\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 0\%  &  11\% & 0\% & 0\%  & 3\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 7\%  &  18\% & 7\% & 7\%  & 7\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 7\%  &  17\% & 1\% & 5\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  16\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  13\% & 0\% & 0\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 7\%  &  16\% & 7\% & 7\%  & 16\%
\\
%
\cmidrule{1-9}
\end{tabular}
}
\end{center}
%
\end{table}

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Second table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% coordinated shock

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks.
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.} 
%
\label{supp2-table6}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf coordinated shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.7,\gamma=0.65$}
&
\multicolumn{3}{c}{$\Phi=0.7,\gamma=0.60$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 35\% \bf & \bf 88\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 97\%  & \bf 100\%  &  \bf 100\% & \bf 81\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 56\%  & \bf 96\%  &  \bf 100\% & \bf 52\% \bf & \bf 96\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 1\%  &  7\% & 0\% \bf & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 0\%  &  5\% & 0\% \bf & 0\%  & 1\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
10\%  & 13\%  &  16\% & 7\% \bf & 7\%  & 9\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
7\%  & 12\%  &  25\% & 1\% \bf & 4\%  & 9\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
26\%  & 32\%  &  49\% & 14\% \bf & 15\%  & 21\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  10\% & 0\% \bf & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
5\%  & 8\%  &  21\% & 3\% \bf & 7\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
13\%  & 18\%  &  30\% & 7\% \bf & 7\%  & 20\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
3\%  & 9\%  &  25\% & 1\% \bf & 3\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 16\%  &  28\% & 8\% \bf & 9\%  & 19\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 31\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 85\%  & \bf 100\%  &  \bf 100\% & \bf 62\% \bf & \bf 97\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 37\%  & \bf 75\%  &  \bf 100\% & \bf 37\% \bf & \bf 75\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 0\%  & 5\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  9\% & 7\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 2\%  &  15\% & 0\% & 0\%  & 5\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
11\%  & 15\%  &  27\% & 7\% & 7\%  & 11\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 7\%  &  18\% & 0\% & 7\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  19\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 4\%  &  17\% & 0\% & 2\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
8\%  & 10\%  &  19\% & 7\% & 8\%  & 17\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 56\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 93\%  & \bf 100\%  &  \bf 100\% & \bf 65\% \bf & \bf 97\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 28\%  & \bf 56\%  &  \bf 97\% & \bf 28\% \bf & \bf 56\%  & \bf 97\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 0\%  & 4\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  7\% & 6\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 0\%  &  15\% & 0\% & 0\%  & 3\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 7\%  &  21\% & 7\% & 7\%  & 7\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 7\%  &  17\% & 0\% & 7\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  16\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  14\% & 0\% & 0\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 8\%  &  16\% & 7\% & 7\%  & 16\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
\end{table}

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Third table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% coordinated shock

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks.
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.} 
%
\label{supp3-table6}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf coordinated shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.8,\gamma=0.75$}
&
\multicolumn{3}{c}{$\Phi=0.8,\gamma=0.70$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 0\%  & \bf 0\%  &  \bf 93\% & \bf 0\% \bf & \bf 0\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 97\%  & \bf 100\%  &  \bf 100\% & \bf 89\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 56\%  & \bf 96\%  &  \bf 100\% & \bf 54\% \bf & \bf 96\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 7\%  &  7\% & 0\% \bf & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  6\% & 0\% \bf & 0\%  & 1\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
12\%  & 15\%  &  19\% & 7\% \bf & 7\%  & 9\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
9\%  & 15\%  &  32\% & 1\% \bf & 5\%  & 11\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
27\%  & 37\%  &  60\% & 14\% \bf & 19\%  & 21\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  10\% & 0\% \bf & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
5\%  & 11\%  &  22\% & 4\% \bf & 7\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
14\%  & 19\%  &  30\% & 7\% \bf & 11\%  & 21\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
3\%  & 11\%  &  27\% & 1\% \bf & 4\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
11\%  & 19\%  &  31\% & 8\% \bf & 9\%  & 21\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 51\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 85\%  & \bf 100\%  &  \bf 100\% & \bf 71\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 37\%  & \bf 75\%  &  \bf 100\% & \bf 37\% \bf & \bf 75\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  1\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 0\%  & 5\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 9\%  &  10\% & 7\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 3\%  &  20\% & 0\% & 0\%  & 6\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
11\%  & 19\%  &  33\% & 7\% & 11\%  & 11\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 7\%  &  19\% & 0\% & 7\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 8\%  &  21\% & 7\% & 7\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 5\%  &  18\% & 0\% & 2\%  & 14\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
8\%  & 10\%  &  23\% & 7\% & 8\%  & 17\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 76\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 93\%  & \bf 100\%  &  \bf 100\% & \bf 76\% \bf & \bf 99\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 28\%  & \bf 56\%  &  \bf 97\% & \bf 28\% \bf & \bf 56\%  & \bf 97\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 99\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 1\%  & 5\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  7\% & 7\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  16\% & 0\% & 0\%  & 6\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 11\%  &  22\% & 7\% & 7\%  & 8\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 7\%  &  17\% & 1\% & 7\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  16\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  14\% & 0\% & 1\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 8\%  &  17\% & 7\% & 7\%  & 16\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
%
\end{table}

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Fourth table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% coordinated shock

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks.
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.} 
%
\label{supp4-table6}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf coordinated shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.9,\gamma=0.85$}
&
\multicolumn{3}{c}{$\Phi=0.9,\gamma=0.80$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 81\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 98\%  & \bf 100\%  &  \bf 100\% & \bf 95\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 0\%  & \bf 0\%  &  \bf 0\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 56\%  & \bf 96\%  &  \bf 100\% & \bf 56\% \bf & \bf 96\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
7\%  & 7\%  &  7\% & 0\% \bf & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% \bf & 0\%  & 1\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
13\%  & 18\%  &  22\% & 7\% \bf & 9\%  & 10\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
11\%  & 17\%  &  37\% & 3\% \bf & 5\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
31\%  & 41\%  &  66\% & 18\% \bf & 19\%  & 25\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  15\% & 0\% \bf & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
5\%  & 11\%  &  25\% & 5\% \bf & 7\%  & 19\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
14\%  & 19\%  &  34\% & 7\% \bf & 12\%  & 23\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
4\%  & 12\%  &  28\% & 2\% \bf & 6\%  & 21\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
17\%  & 21\%  &  33\% & 8\% \bf & 11\%  & 23\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 75\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 85\%  & \bf 100\%  &  \bf 100\% & \bf 78\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 0\%  & \bf 0\%  &  \bf 0\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 37\%  & \bf 75\%  &  \bf 100\% & \bf 37\% \bf & \bf 75\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  1\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 0\%  & 6\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 9\%  &  10\% & 7\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 4\%  &  25\% & 0\% & 1\%  & 7\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
14\%  & 22\%  &  41\% & 7\% & 11\%  & 15\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 7\%  &  21\% & 0\% & 7\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 8\%  &  23\% & 7\% & 7\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 5\%  &  19\% & 1\% & 3\%  & 15\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 11\%  &  23\% & 7\% & 9\%  & 17\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 93\%  & \bf 93\%  &  \bf 93\% & \bf 93\% \bf & \bf 93\%  & \bf 93\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 0\%  & \bf 0\%  &  \bf 100\% & \bf 85\% \bf & \bf 99\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 0\%  & \bf 0\%  &  \bf 0\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 28\%  & \bf 56\%  &  \bf 97\% & \bf 28\% \bf & \bf 56\%  & \bf 97\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  0\% & 0\% & 0\%  & 0\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  7\% & 0\% & 1\%  & 6\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  7\% & 7\% & 7\%  & 7\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  17\% & 0\% & 0\%  & 10\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 11\%  &  24\% & 7\% & 7\%  & 10\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 7\%  &  17\% & 1\% & 7\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  17\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  14\% & 0\% & 1\%  & 13\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 8\%  &  17\% & 7\% & 7\%  & 16\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
%
\end{table}


\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% random shock

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks.
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.} 
%
\label{supp1-table7}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf idiosyncratic shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.6,\gamma=0.55$}
&
\multicolumn{3}{c}{$\Phi=0.6,\gamma=0.50$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 53\% \bf & \bf 87\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 62\% \bf & \bf 95\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 58\%  &  \bf 60\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 54\%  & \bf 100\%  &  \bf 100\% & \bf 45\% \bf & \bf 90\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
2\%  & 4\%  &  16\% & 1\% \bf & 3\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 1\%  &  14\% & 0\% \bf & 0\%  & 5\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
8\%  & 11\%  &  23\% & 5\% \bf & 7\%  & 12\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 7\%  &  24\% & 0\% \bf & 2\%  & 11\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 21\%  &  39\% & 7\% \bf & 15\%  & 25\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 3\%  &  13\% & 1\% \bf & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
7\%  & 14\%  &  25\% & 5\% \bf & 10\%  & 19\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
11\%  & 21\%  &  34\% & 7\% \bf & 11\%  & 23\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 11\%  &  21\% & 0\% \bf & 9\%  & 18\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
10\%  & 15\%  &  27\% & 7\% \bf & 9\%  & 19\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 94\%  &  \bf 95\% & \bf 69\% \bf & \bf 92\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 77\%  & \bf 100\%  &  \bf 100\% & \bf 45\% \bf & \bf 87\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 57\%  &  \bf 57\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 36\%  & \bf 81\%  &  \bf 100\% & \bf 34\% \bf & \bf 75\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 95\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 2\%  &  13\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 2\%  &  17\% & 0\% & 1\%  & 13\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  18\% & 7\% & 7\%  & 15\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  25\% & 0\% & 3\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
11\%  & 19\%  &  32\% & 7\% & 12\%  & 22\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
5\%  & 9\%  &  19\% & 1\% & 8\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
8\%  & 13\%  &  23\% & 7\% & 9\%  & 19\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 3\%  &  19\% & 0\% & 1\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 9\%  &  20\% & 7\% & 8\%  & 17\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 93\% \bf & \bf 95\%  & \bf 96\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 96\%  & \bf 100\%  &  \bf 100\% & \bf 48\% \bf & \bf 89\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 57\%  &  \bf 57\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 34\%  & \bf 70\%  &  \bf 100\% & \bf 31\% \bf & \bf 67\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 93\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  12\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 4\%  &  16\% & 0\% & 1\%  & 10\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  16\% & 5\% & 7\%  & 12\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 8\%  &  25\% & 0\% & 3\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 17\%  &  29\% & 7\% & 11\%  & 21\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
0\%  & 0\%  &  9\% & 0\% & 0\%  & 9\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
7\%  & 8\%  &  17\% & 3\% & 7\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 9\%  &  18\% & 7\% & 7\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  17\% & 0\% & 0\%  & 16\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 8\%  &  17\% & 7\% & 7\%  & 16\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
%
\end{table}

\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Second table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% random shock

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks. 
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.} 
%
\label{supp2-table7}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf idiosyncratic shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.7,\gamma=0.65$}
&
\multicolumn{3}{c}{$\Phi=0.7,\gamma=0.60$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 96\% & \bf 73\% \bf & \bf 94\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 81\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 59\%  &  \bf 60\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 55\%  & \bf 100\%  &  \bf 100\% & \bf 55\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
3\%  & 7\%  &  17\% & 1\% \bf & 2\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 5\%  &  21\% & 0\% \bf & 3\%  & 13\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
10\%  & 18\%  &  28\% & 7\% \bf & 9\%  & 19\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
7\%  & 9\%  &  26\% & 0\% \bf & 3\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
13\%  & 24\%  &  41\% & 9\% \bf & 16\%  & 27\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 3\%  &  14\% & 1\% \bf & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
7\%  & 15\%  &  27\% & 7\% \bf & 10\%  & 20\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
13\%  & 23\%  &  35\% & 7\% \bf & 13\%  & 25\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 11\%  &  23\% & 0\% \bf & 6\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
11\%  & 17\%  &  29\% & 7\% \bf & 9\%  & 20\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 79\% \bf & \bf 95\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 77\%  & \bf 100\%  &  \bf 100\% & \bf 57\% \bf & \bf 97\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 57\%  &  \bf 57\% & \bf 57\% & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 37\%  & \bf 78\%  &  \bf 100\% & \bf 35\% \bf & \bf 76\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 3\%  &  13\% & 1\% & 1\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 4\%  &  17\% & 0\% & 1\%  & 14\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 9\%  &  19\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 10\%  &  25\% & 0\% & 3\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 18\%  &  33\% & 8\% & 15\%  & 25\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  11\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
6\%  & 11\%  &  21\% & 3\% & 9\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 15\%  &  25\% & 7\% & 9\%  & 19\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 3\%  &  19\% & 0\% & 1\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 10\%  &  21\% & 7\% & 8\%  & 17\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 85\% \bf & \bf 95\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 96\%  & \bf 100\%  &  \bf 100\% & \bf 67\% \bf & \bf 98\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 57\%  &  \bf 57\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 33\%  & \bf 71\%  &  \bf 100\% & \bf 33\% \bf & \bf 69\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 99\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  12\% & 1\% & 1\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 5\%  &  16\% & 0\% & 2\%  & 13\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  16\% & 6\% & 7\%  & 15\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  25\% & 0\% & 3\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 17\%  &  31\% & 7\% & 13\%  & 21\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  11\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
7\%  & 8\%  &  17\% & 3\% & 7\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 9\%  &  19\% & 7\% & 8\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 3\%  &  17\% & 0\% & 1\%  & 16\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 8\%  &  17\% & 7\% & 7\%  & 16\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
%
\end{table}


\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Third table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% random shock

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks. 
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.} 
%
\label{supp3-table7}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%%%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf idiosyncratic shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.8,\gamma=0.75$}
&
\multicolumn{3}{c}{$\Phi=0.8,\gamma=0.70$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 83\% \bf & \bf 94\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 89\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 60\%  &  \bf 63\% & \bf 57\% \bf & \bf 57\%  & \bf 58\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 55\%  & \bf 100\%  &  \bf 100\% & \bf 52\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
4\%  & 9\%  &  21\% & 1\% \bf & 2\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 7\%  &  21\% & 0\% \bf & 1\%  & 15\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
10\%  & 21\%  &  31\% & 7\% \bf & 9\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 11\%  &  27\% & 0\% \bf & 5\%  & 20\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 23\%  &  43\% & 9\% \bf & 17\%  & 31\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
2\%  & 5\%  &  15\% & 1\% \bf & 1\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
8\%  & 18\%  &  29\% & 7\% \bf & 11\%  & 21\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
15\%  & 25\%  &  38\% & 7\% \bf & 15\%  & 27\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 12\%  &  23\% & 0\% \bf & 7\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
12\%  & 21\%  &  33\% & 7\% \bf & 10\%  & 22\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 84\% \bf & \bf 94\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 78\%  & \bf 100\%  &  \bf 100\% & \bf 68\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 57\%  &  \bf 59\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 37\%  & \bf 79\%  &  \bf 100\% & \bf 35\% \bf & \bf 81\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 3\%  &  13\% & 1\% & 1\%  & 13\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 4\%  &  17\% & 0\% & 3\%  & 15\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 9\%  &  21\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  25\% & 0\% & 4\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
10\%  & 19\%  &  35\% & 7\% & 17\%  & 25\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 2\%  &  13\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
5\%  & 12\%  &  21\% & 5\% & 9\%  & 19\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
9\%  & 16\%  &  28\% & 7\% & 11\%  & 20\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 4\%  &  19\% & 0\% & 1\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
8\%  & 11\%  &  23\% & 7\% & 8\%  & 17\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 96\% & \bf 92\% \bf & \bf 95\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 96\%  & \bf 100\%  &  \bf 100\% & \bf 73\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 57\%  & \bf 57\%  &  \bf 57\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 33\%  & \bf 67\%  &  \bf 100\% & \bf 31\% \bf & \bf 69\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  12\% & 1\% & 1\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 5\%  &  16\% & 1\% & 3\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 7\%  &  17\% & 7\% & 7\%  & 15\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  25\% & 0\% & 7\%  & 22\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 17\%  &  31\% & 7\% & 13\%  & 25\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  11\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
7\%  & 8\%  &  18\% & 6\% & 7\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 9\%  &  20\% & 7\% & 8\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 2\%  &  17\% & 0\% & 1\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 8\%  &  17\% & 7\% & 7\%  & 17\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
%
\end{table}

\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Fourth table for analysis of residual instability of homogeneous versus heterogeneous networks
%%% random shock

\begin{table}
%
\caption{Residual instabilities of homogeneous versus heterogeneous networks under coordinated shocks. 
The percentages shown are the percentages of networks for which $\xi<0.05$ or $\xi<0.1$ or $\xi<0.2$.} 
%
\label{supp4-table7}
%
\begin{center}
\scalebox{0.75}[0.8]
{%%%%%\small
%
\begin{tabular}{c c r      r r r | r r r}
&
&
&
\multicolumn{6}{c}{\bf idiosyncratic shock}
\\
&
&
&
\multicolumn{3}{c|}{$\Phi=0.9,\gamma=0.85$}
&
\multicolumn{3}{c}{$\Phi=0.9,\gamma=0.80$}
\\
&
&
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c|}{${\xi<0.2}$}
&
\multicolumn{1}{c}{${\xi<0.05}$}
&
\multicolumn{1}{c}{${\xi<0.1}$}
&
\multicolumn{1}{c}{${\xi<0.2}$}
\\
\cline{1-9}
\multirow{15}{*}{${|V|=50}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 93\% \bf & \bf 94\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 96\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 5\%  & \bf 5\%  &  \bf 8\% & \bf 57\% \bf & \bf 57\%  & \bf 59\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 55\%  & \bf 100\%  &  \bf 100\% & \bf 53\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
9\%  & 11\%  &  21\% & 1\% \bf & 3\%  & 14\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
1\%  & 9\%  &  23\% & 0\% \bf & 2\%  & 14\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
11\%  & 21\%  &  31\% & 7\% \bf & 10\%  & 22\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 11\%  &  27\% & 0\% \bf & 7\%  & 20\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
12\%  & 23\%  &  44\% & 9\% \bf & 20\%  & 35\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
2\%  & 4\%  &  15\% & 1\% \bf & 2\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
8\%  & 17\%  &  31\% & 7\% \bf & 12\%  & 22\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
17\%  & 25\%  &  39\% & 9\% \bf & 17\%  & 29\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
1\%  & 12\%  &  25\% & 0\% \bf & 8\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
17\%  & 23\%  &  35\% & 9\% \bf & 13\%  & 23\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=100}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 92\% \bf & \bf 95\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 77\%  & \bf 100\%  &  \bf 100\% & \bf 74\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 3\%  & \bf 3\%  &  \bf 5\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 34\%  & \bf 81\%  &  \bf 100\% & \bf 37\% \bf & \bf 81\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 3\%  &  14\% & 1\% & 1\%  & 12\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 6\%  &  19\% & 0\% & 1\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 13\%  &  22\% & 7\% & 7\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  25\% & 0\% & 6\%  & 19\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
11\%  & 21\%  &  37\% & 7\% & 17\%  & 29\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 2\%  &  13\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
6\%  & 13\%  &  23\% & 5\% & 9\%  & 19\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
9\%  & 19\%  &  31\% & 7\% & 11\%  & 21\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 5\%  &  21\% & 0\% & 2\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
9\%  & 14\%  &  25\% & 7\% & 8\%  & 18\%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hline
\multirow{15}{*}{${|V|=300}$}
&
\multirow{5}{*}{homogeneous} 
&
in-arborescence
&  
\bf 94\%  & \bf 95\%  &  \bf 95\% & \bf 94\% \bf & \bf 95\%  & \bf 95\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
\bf 0\%  & \bf 0\%  &  \bf 100\% & \bf 85\% \bf & \bf 100\%  & \bf 100\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
\bf 3\%  & \bf 3\%  &  \bf 3\% & \bf 57\% \bf & \bf 57\%  & \bf 57\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
\bf 30\%  & \bf 69\%  &  \bf 100\% & \bf 31\% \bf & \bf 69\%  & \bf 100\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
\bf 100\%  & \bf 100\%  &  \bf 100\% & \bf 100\% \bf & \bf 100\%  & \bf 100\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.1,0.95)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  12\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
0\%  & 5\%  &  17\% & 0\% & 3\%  & 16\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 8\%  &  17\% & 7\% & 7\%  & 16\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 9\%  &  25\% & 0\% & 7\%  & 22\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
10\%  & 17\%  &  33\% & 6\% & 15\%  & 25\%
\\
\cline{2-9}
& 
\multirow{5}{*}{${(0.2,0.6)}$-heterogeneous}
&
in-arborescence
&  
1\%  & 1\%  &  11\% & 1\% & 1\%  & 11\%
\\
&
&
{\sf ER}, average degree $3$ 
&  
7\%  & 9\%  &  18\% & 6\% & 7\%  & 17\%
\\
&
&
{\sf ER}, average degree $6$ 
&  
7\%  & 10\%  &  21\% & 7\% & 9\%  & 17\%
\\
&
&
{\sf SF}, average degree $3$ 
&  
0\%  & 1\%  &  17\% & 0\% & 1\%  & 17\%
\\
&
&
{\sf SF}, average degree $6$ 
&  
7\%  & 9\%  &  17\% & 7\% & 7\%  & 16\%
\\
%
\cline{1-9}
\end{tabular}
}
\end{center}
%
\end{table}





\renewcommand{\thefigure}{S\arabic{figure}}
\setcounter{figure}{0}

%%\clearpage
\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig1 
%%\input{../tex-figures/newfig1-coordinated-only.tex}

\begin{figure}
%
\vspace*{0.7in}
%%\hspace*{-0.0in}
\renewcommand{\thesubfigure}{\hspace*{0.6in}\protect\raisebox{0.2in}[0in][0.0in]{(\Alph{subfigure})}}
{
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(1.3,-1.8)(3.3,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.50)(0.46,1.50)
\rput[mr](0.70,1.55){\bf\normalsize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.50)(1.16,1.50)
\rput[mr](1.40,1.55){\bf\normalsize {\sf ER} model (average degree $3$), coordinated shock}
%%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.43)(0.46,1.43)
%\rput[mr](0.7,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), random shock}
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](1.11,1.43)(1.16,1.43)
%\rput[mr](1.40,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.41,1.36)(0.46,1.36)
\rput[mr](0.7,1.41){\bf\normalsize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](1.11,1.36)(1.16,1.36)
\rput[mr](1.40,1.41){\bf\normalsize {\sf SF} model (average degree $3$), coordinated shock}
%%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.41,1.29)(0.46,1.29)
%\rput[mr](0.7,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), random shock}
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.29)(1.16,1.29)
%\rput[mr](1.40,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.22)(0.76,1.22)
\rput[mr](1,1.27){\bf\normalsize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.15)(0.76,1.15)
%\rput[mr](1,1.20){\bf\footnotesize in-arborescence (average degree $\approx 1$), random shock}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.002)(0.15,0.006)(0.20,0.012)(0.25,0.02)(0.30,0.03)(0.35,0.034)(0.40,0.056)(0.45,0.136)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.008)(0.15,0.014)(0.20,0.024)(0.25,0.04)(0.30,0.048)(0.35,0.066)(0.40,0.112)(0.45,0.314)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.004)(0.15,0.004)(0.20,0.016)(0.25,0.014)(0.30,0.022)(0.35,0.034)(0.40,0.128)(0.45,0.118)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.012)(0.15,0.012)(0.20,0.024)(0.25,0.026)(0.30,0.046)(0.35,0.232)(0.40,0.158)(0.45,0.676)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.00)(0.15,0.002)(0.20,0.004)(0.25,0.004)(0.30,0.006)(0.35,0.014)(0.40,0.0118)(0.45,0.692)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.008)(0.15,0.01)(0.20,0.01)(0.25,0.026)(0.30,0.048)(0.35,0.294)(0.40,0.382)(0.45,0.854)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.004)(0.15,0.004)(0.20,0.016)(0.25,0.014)(0.30,0.022)(0.35,0.024)(0.40,0.128)(0.45,0.118)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.012)(0.15,0.012)(0.20,0.024)(0.25,0.026)(0.30,0.046)(0.35,0.232)(0.40,0.158)(0.45,0.676)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.058)(0.15,0.078)(0.20,0.10)(0.25,0.184)(0.30,0.356)(0.35,0.472)(0.40,0.582)(0.45,0.74)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.006)(0.15,0.018)(0.20,0.016)(0.25,0.026)(0.30,0.096)(0.35,0.164)(0.40,0.106)(0.45,0.120)
\end{pspicture}
 }
}
\hspace*{1in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(-0.8,-1.8)(0.8,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.01)(0.15,0.03)(0.20,0.066)(0.25,0.10)(0.30,0.144)(0.35,0.202)(0.40,0.318)(0.45,0.666)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.014)(0.10,0.040)(0.15,0.072)(0.20,0.014)(0.25,0.174)(0.30,0.236)(0.35,0.354)(0.40,0.516)(0.45,0.746)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.004)(0.15,0.022)(0.20,0.054)(0.25,0.078)(0.30,0.204)(0.35,0.19)(0.40,0.426)(0.45,0.902)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.022)(0.10,0.044)(0.15,0.062)(0.20,0.112)(0.25,0.182)(0.30,0.29)(0.35,0.438)(0.40,0.674)(0.45,0.832)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.006)(0.15,0.012)(0.20,0.052)(0.25,0.086)(0.30,0.144)(0.35,0.178)(0.40,0.498)(0.45,0.782)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.042)(0.10,0.048)(0.15,0.092)(0.20,0.232)(0.25,0.22)(0.30,0.350)(0.35,0.518)(0.40,0.70)(0.45,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.014)(0.15,0.022)(0.20,0.078)(0.25,0.122)(0.30,0.158)(0.35,0.196)(0.40,0.334)(0.45,0.592)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.032)(0.10,0.04)(0.15,0.106)(0.20,0.232)(0.25,0.184)(0.30,0.332)(0.35,0.484)(0.40,0.546)(0.45,0.764)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.092)(0.15,0.15)(0.20,0.354)(0.25,0.452)(0.30,0.766)(0.35,1)(0.40,1)(0.45,1)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[origin={-0.05,0},linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.014)(0.10,0.048)(0.15,0.082)(0.20,0.144)(0.25,0.21)(0.30,0.42)(0.35,0.592)(0.40,0.554)(0.45,0.762)
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(-0.8,-1.8)(0.8,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.006)(0.15,0.026)(0.20,0.038)(0.25,0.068)(0.30,0.082)(0.35,0.118)(0.40,0.168)(0.45,0.392)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.028)(0.15,0.05)(0.20,0.084)(0.25,0.116)(0.30,0.142)(0.35,0.176)(0.40,0.350)(0.45,0.582)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.004)(0.15,0.016)(0.20,0.034)(0.25,0.084)(0.30,0.090)(0.35,0.104)(0.40,0.404)(0.45,0.78)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.014)(0.10,0.03)(0.15,0.042)(0.20,0.086)(0.25,0.12)(0.30,0.228)(0.35,0.314)(0.40,0.742)(0.45,0.738)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.002)(0.15,0.006)(0.20,0.018)(0.25,0.038)(0.30,0.046)(0.35,0.17)(0.40,0.21)(0.45,0.714)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.008)(0.10,0.028)(0.15,0.04)(0.20,0.056)(0.25,0.08)(0.30,0.102)(0.35,0.142)(0.40,0.536)(0.45,0.746)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.014)(0.15,0.026)(0.20,0.044)(0.25,0.098)(0.30,0.108)(0.35,0.118)(0.40,0.178)(0.45,0.364)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.024)(0.10,0.046)(0.15,0.078)(0.20,0.096)(0.25,0.138)(0.30,0.142)(0.35,0.162)(0.40,0.362)(0.45,0.606)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.04)(0.10,0.158)(0.15,0.20)(0.20,0.20)(0.25,0.20)(0.30,0.246)(0.35,0.452)(0.40,0.804)(0.45,0.934)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.048)(0.15,0.068)(0.20,0.20)(0.25,0.20)(0.30,0.232)(0.35,0.306)(0.40,0.316)(0.45,0.444)
%
\end{pspicture}
}
}
%%%
\\
\hspace*{-0.0in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\renewcommand{\thesubfigure}{\hspace*{0.6in}\protect\raisebox{0.2in}[0in][0.0in]{(\Alph{subfigure})}}
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(1,-1.8)(3,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.002)(0.15,0.007)(0.20,0.016)(0.25,0.022)(0.30,0.028)(0.35,0.036)(0.40,0.051)(0.45,0.14)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.007)(0.10,0.011)(0.15,0.015)(0.20,0.028)(0.25,0.043)(0.30,0.046)(0.35,0.063)(0.40,0.108)(0.45,0.234)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.001)(0.15,0.003)(0.20,0.007)(0.25,0.015)(0.30,0.039)(0.35,0.039)(0.40,0.241)(0.45,0.148)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.008)(0.15,0.016)(0.20,0.032)(0.25,0.036)(0.30,0.046)(0.35,0.228)(0.40,0.58)(0.45,0.679)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.00)(0.15,0.001)(0.20,0.003)(0.25,0.005)(0.30,0.012)(0.35,0.015)(0.40,0.226)(0.45,0.705)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.005)(0.15,0.008)(0.20,0.014)(0.25,0.036)(0.30,0.047)(0.35,0.288)(0.40,0.441)(0.45,0.696)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.004)(0.15,0.004)(0.20,0.02)(0.25,0.018)(0.30,0.037)(0.35,0.049)(0.40,0.145)(0.45,0.34)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.008)(0.10,0.005)(0.15,0.006)(0.20,0.037)(0.25,0.054)(0.30,0.059)(0.35,0.054)(0.40,0.13)(0.45,0.344)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.054)(0.15,0.081)(0.20,0.112)(0.25,0.135)(0.30,0.405)(0.35,0.51)(0.40,0.608)(0.45,0.763)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.003)(0.10,0.01)(0.15,0.011)(0.20,0.014)(0.25,0.039)(0.30,0.094)(0.35,0.103)(0.40,0.135)(0.45,0.262)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
\hspace*{1in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.011)(0.15,0.029)(0.20,0.057)(0.25,0.107)(0.30,0.151)(0.35,0.205)(0.40,0.32)(0.45,0.673)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.027)(0.10,0.051)(0.15,0.082)(0.20,0.143)(0.25,0.215)(0.30,0.264)(0.35,0.381)(0.40,0.547)(0.45,0.76)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.008)(0.15,0.025)(0.20,0.046)(0.25,0.101)(0.30,0.157)(0.35,0.357)(0.40,0.629)(0.45,0.687)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.034)(0.10,0.058)(0.15,0.09)(0.20,0.217)(0.25,0.204)(0.30,0.40)(0.35,0.60)(0.40,0.735)(0.45,0.844)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.015)(0.15,0.023)(0.20,0.084)(0.25,0.122)(0.30,0.181)(0.35,0.203)(0.40,0.421)(0.45,0.712)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.052)(0.10,0.053)(0.15,0.081)(0.20,0.209)(0.25,0.272)(0.30,0.288)(0.35,0.453)(0.40,0.529)(0.45,0.784)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.008)(0.15,0.025)(0.20,0.046)(0.25,0.101)(0.30,0.157)(0.35,0.357)(0.40,0.629)(0.45,0.687)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.034)(0.10,0.058)(0.15,0.09)(0.20,0.217)(0.25,0.204)(0.30,0.40)(0.35,0.60)(0.40,0.735)(0.45,0.844)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.035)(0.10,0.076)(0.15,0.152)(0.20,0.296)(0.25,0.366)(0.30,0.769)(0.35,1)(0.40,1)(0.45,1)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.016)(0.10,0.035)(0.15,0.059)(0.20,0.142)(0.25,0.20)(0.30,0.38)(0.35,0.562)(0.40,0.576)(0.45,0.63)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.003)(0.10,0.007)(0.15,0.024)(0.20,0.044)(0.25,0.069)(0.30,0.09)(0.35,0.12)(0.40,0.178)(0.45,0.473)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.012)(0.10,0.035)(0.15,0.057)(0.20,0.087)(0.25,0.115)(0.30,0.144)(0.35,0.193)(0.40,0.304)(0.45,0.592)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.006)(0.15,0.02)(0.20,0.039)(0.25,0.072)(0.30,0.081)(0.35,0.108)(0.40,0.255)(0.45,0.819)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.01)(0.10,0.042)(0.15,0.059)(0.20,0.16)(0.25,0.116)(0.30,0.228)(0.35,0.46)(0.40,0.736)(0.45,0.705)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.003)(0.15,0.022)(0.20,0.031)(0.25,0.068)(0.30,0.085)(0.35,0.105)(0.40,0.297)(0.45,0.641)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.016)(0.10,0.129)(0.15,0.069)(0.20,0.244)(0.25,0.125)(0.30,0.137)(0.35,0.169)(0.40,0.371)(0.45,0.595)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.011)(0.15,0.031)(0.20,0.049)(0.25,0.10)(0.30,0.129)(0.35,0.145)(0.40,0.257)(0.45,0.258)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.011)(0.10,0.079)(0.15,0.08)(0.20,0.186)(0.25,0.156)(0.30,0.176)(0.35,0.255)(0.40,0.335)(0.45,0.533)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.042)(0.10,0.14)(0.15,0.20)(0.20,0.20)(0.25,0.20)(0.30,0.244)(0.35,0.445)(0.40,0.84)(0.45,0.953)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.005)(0.10,0.033)(0.15,0.095)(0.20,0.20)(0.25,0.20)(0.30,0.219)(0.35,0.278)(0.40,0.401)(0.45,0.367)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 7 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{0.6in}(\Alph{subfigure})}
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(1,-1.8)(3,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psset{origin={-0.05,0}}
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.00)(0.15,0.006)(0.20,0.011)(0.25,0.02)(0.30,0.028)(0.35,0.035)(0.40,0.147)(0.45,0.211)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.005)(0.10,0.013)(0.15,0.017)(0.20,0.026)(0.25,0.039)(0.30,0.049)(0.35,0.071)(0.40,0.113)(0.45,0.239)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.002)(0.15,0.006)(0.20,0.01)(0.25,0.02)(0.30,0.029)(0.35,0.125)(0.40,0.428)(0.45,0.81)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.012)(0.15,0.018)(0.20,0.027)(0.25,0.034)(0.30,0.125)(0.35,0.39)(0.40,0.836)(0.45,0.811)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.003)(0.15,0.004)(0.20,0.012)(0.25,0.019)(0.30,0.026)(0.35,0.115)(0.40,0.331)(0.45,0.772)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.008)(0.10,0.01)(0.15,0.013)(0.20,0.037)(0.25,0.049)(0.30,0.057)(0.35,0.161)(0.40,0.588)(0.45,0.711)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.012)(0.15,0.04)(0.20,0.062)(0.25,0.11)(0.30,0.133)(0.35,0.148)(0.40,0.174)(0.45,0.294)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.011)(0.10,0.011)(0.15,0.011)(0.20,0.038)(0.25,0.057)(0.30,0.054)(0.35,0.055)(0.40,0.206)(0.45,0.538)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.019)(0.10,0.051)(0.15,0.075)(0.20,0.101)(0.25,0.145)(0.30,0.415)(0.35,0.531)(0.40,0.645)(0.45,0.82)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.003)(0.10,0.006)(0.15,0.008)(0.20,0.017)(0.25,0.03)(0.30,0.071)(0.35,0.104)(0.40,0.172)(0.45,0.176)
%
\psset{origin={0,0}}
%
\end{pspicture}
 }
}
\hspace*{1in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 8 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.009)(0.15,0.027)(0.20,0.058)(0.25,0.111)(0.30,0.152)(0.35,0.202)(0.40,0.384)(0.45,0.665)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.023)(0.10,0.053)(0.15,0.084)(0.20,0.14)(0.25,0.206)(0.30,0.272)(0.35,0.38)(0.40,0.54)(0.45,0.781)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.009)(0.15,0.028)(0.20,0.059)(0.25,0.115)(0.30,0.139)(0.35,0.356)(0.40,0.819)(0.45,0.874)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.027)(0.10,0.051)(0.15,0.08)(0.20,0.208)(0.25,0.263)(0.30,0.613)(0.35,0.772)(0.40,0.799)(0.45,0.807)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.024)(0.15,0.031)(0.20,0.104)(0.25,0.152)(0.30,0.196)(0.35,0.283)(0.40,0.514)(0.45,0.788)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.075)(0.10,0.077)(0.15,0.081)(0.20,0.248)(0.25,0.307)(0.30,0.32)(0.35,0.404)(0.40,0.612)(0.45,0.822)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.026)(0.15,0.029)(0.20,0.102)(0.25,0.151)(0.30,0.199)(0.35,0.221)(0.40,0.376)(0.45,0.654)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.067)(0.10,0.063)(0.15,0.064)(0.20,0.289)(0.25,0.271)(0.30,0.273)(0.35,0.385)(0.40,0.488)(0.45,0.763)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.02)(0.10,0.07)(0.15,0.14)(0.20,0.284)(0.25,0.368)(0.30,0.75)(0.35,0.981)(0.40,0.992)(0.45,1)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.01)(0.10,0.034)(0.15,0.063)(0.20,0.145)(0.25,0.189)(0.30,0.341)(0.35,0.513)(0.40,0.618)(0.45,0.658)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 9 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%
\subfigure[]{
\scalebox{0.7}[0.6]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.007)(0.15,0.016)(0.20,0.039)(0.25,0.073)(0.30,0.098)(0.35,0.124)(0.40,0.251)(0.45,0.484)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.012)(0.10,0.037)(0.15,0.06)(0.20,0.088)(0.25,0.124)(0.30,0.147)(0.35,0.192)(0.40,0.31)(0.45,0.573)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.007)(0.15,0.018)(0.20,0.04)(0.25,0.067)(0.30,0.092)(0.35,0.125)(0.40,0.571)(0.45,0.898)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.01)(0.10,0.034)(0.15,0.054)(0.20,0.083)(0.25,0.202)(0.30,0.361)(0.35,0.739)(0.40,0.874)(0.45,0.797)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.01)(0.15,0.029)(0.20,0.053)(0.25,0.101)(0.30,0.12)(0.35,0.137)(0.40,0.218)(0.45,0.748)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.028)(0.10,0.085)(0.15,0.108)(0.20,0.114)(0.25,0.172)(0.30,0.176)(0.35,0.208)(0.40,0.354)(0.45,0.539)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.012)(0.15,0.04)(0.20,0.062)(0.25,0.11)(0.30,0.133)(0.35,0.148)(0.40,0.174)(0.45,0.294)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.027)(0.10,0.088)(0.15,0.115)(0.20,0.194)(0.25,0.172)(0.30,0.175)(0.35,0.25)(0.40,0.302)(0.45,0.563)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.12)(0.15,0.185)(0.20,0.20)(0.25,0.20)(0.30,0.25)(0.35,0.433)(0.40,0.803)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.005)(0.10,0.037)(0.15,0.087)(0.20,0.192)(0.25,0.197)(0.30,0.215)(0.35,0.274)(0.40,0.377)(0.45,0.382)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
}
%%%%
\vspace*{-0.3in}
\caption{\label{newfig1}Effect of variations of equity to asset ratio (with respect to shock) on the vulnerability index $\xi$ for homogeneous networks.
Lower values of $\xi$ imply higher global stability of a network.
}
%
\end{figure}

%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



















\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig2
%%\input{../tex-figures/newfig2-coordinated-only.tex}

\begin{figure}
%
\vspace*{0.5in}
%%\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1.5,-1.8)(3.5,9)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(A)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.50)(0.46,1.50)
\rput[mr](0.70,1.55){\bf\normalsize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.50)(1.16,1.50)
\rput[mr](1.40,1.55){\bf\normalsize {\sf ER} model (average degree $3$), coordinated shock}
%%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.43)(0.46,1.43)
%%\rput[mr](0.7,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), random shock}
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](1.11,1.43)(1.16,1.43)
%%\rput[mr](1.40,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.41,1.36)(0.46,1.36)
\rput[mr](0.7,1.41){\bf\normalsize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](1.11,1.36)(1.16,1.36)
\rput[mr](1.40,1.41){\bf\normalsize {\sf SF} model (average degree $3$), coordinated shock}
%%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.41,1.29)(0.46,1.29)
%%\rput[mr](0.7,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), random shock}
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.29)(1.16,1.29)
%%\rput[mr](1.40,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.22)(0.76,1.22)
\rput[mr](1,1.27){\bf\normalsize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.15)(0.76,1.15)
%%\rput[mr](1,1.20){\bf\footnotesize in-arborescence (average degree $\approx 1$), random shock}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.476)(0.10,0.85)(0.15,0.95)(0.20,0.974)(0.25,0.986)(0.30,0.994)(0.35,0.996)(0.40,0.998)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.548)(0.10,0.798)(0.15,0.864)(0.20,0.89)(0.25,0.91)(0.30,0.918)(0.35,0.928)(0.40,0.936)(0.45,0.944)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.122)(0.10,0.176)(0.15,0.178)(0.20,0.242)(0.25,0.346)(0.30,0.358)(0.35,0.238)(0.40,0.332)(0.45,0.67)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.136)(0.10,0.26)(0.15,0.252)(0.20,0.234)(0.25,0.204)(0.30,0.20)(0.35,0.326)(0.40,0.496)(0.45,0.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.078)(0.10,0.684)(0.15,0.952)(0.20,0.984)(0.25,0.994)(0.30,1.00)(0.35,1.00)(0.40,1.00)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.12)(0.10,0.616)(0.15,0.752)(0.20,0.802)(0.25,0.836)(0.30,0.808)(0.35,0.814)(0.40,0.82)(0.45,0.898)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.054)(0.10,0.11)(0.15,0.136)(0.20,0.304)(0.25,0.274)(0.30,0.382)(0.35,0.33)(0.40,0.326)(0.45,0.454)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.084)(0.10,0.08)(0.15,0.178)(0.20,0.186)(0.25,0.168)(0.30,0.208)(0.35,0.102)(0.40,0.192)(0.45,0.39)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.516)(0.10,0.738)(0.15,0.828)(0.20,0.848)(0.25,0.87)(0.30,0.88)(0.35,0.896)(0.40,0.904)(0.45,0.942)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.148)(0.10,0.142)(0.15,0.176)(0.20,0.168)(0.25,0.216)(0.30,0.25)(0.35,0.164)(0.40,0.30)(0.45,0.234)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{1in}
%%%%%%%%%%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,8)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(B)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%
\psset{origin={-0.05,0.0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.56)(0.10,0.892)(0.15,0.974)(0.20,0.992)(0.25,1.00)(0.30,1.00)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.548)(0.10,0.798)(0.15,0.864)(0.20,0.89)(0.25,0.91)(0.30,0.918)(0.35,0.928)(0.40,0.936)(0.45,0.944)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.442)(0.10,0.644)(0.15,0.696)(0.20,0.776)(0.25,0.836)(0.30,0.886)(0.35,0.878)(0.40,0.888)(0.45,0.93)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.478)(0.10,0.596)(0.15,0.676)(0.20,0.70)(0.25,0.696)(0.30,0.75)(0.35,0.766)(0.40,0.816)(0.45,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.078)(0.10,0.916)(0.15,0.988)(0.20,0.99)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.36)(0.10,0.814)(0.15,0.882)(0.20,0.888)(0.25,0.94)(0.30,0.926)(0.35,0.94)(0.40,0.942)(0.45,0.946)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.232)(0.10,0.478)(0.15,0.734)(0.20,0.752)(0.25,0.826)(0.30,0.936)(0.35,0.912)(0.40,0.966)(0.45,0.896)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.408)(0.10,0.602)(0.15,0.646)(0.20,0.712)(0.25,0.768)(0.30,0.718)(0.35,0.684)(0.40,0.806)(0.45,0.854)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.606)(0.10,0.646)(0.15,0.646)(0.20,0.646)(0.25,0.646)(0.30,0.758)(0.35,0.862)(0.40,0.94)(0.45,0.992)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.568)(0.10,0.648)(0.15,0.646)(0.20,0.664)(0.25,0.652)(0.30,0.716)(0.35,0.702)(0.40,0.792)(0.45,0.82)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-2.8)(0.8,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(C)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.764)(0.10,0.978)(0.15,0.988)(0.20,0.996)(0.25,0.996)(0.30,0.998)(0.35,0.998)(0.40,0.996)(0.45,0.994)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.716)(0.10,0.856)(0.15,0.894)(0.20,0.91)(0.25,0.922)(0.30,0.924)(0.35,0.92)(0.40,0.912)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.238)(0.10,0.444)(0.15,0.544)(0.20,0.68)(0.25,0.702)(0.30,0.742)(0.35,0.638)(0.40,0.83)(0.45,0.892)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.242)(0.10,0.262)(0.15,0.452)(0.20,0.51)(0.25,0.40)(0.30,0.446)(0.35,0.742)(0.40,0.544)(0.45,0.728)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.624)(0.10,0.97)(0.15,0.996)(0.20,1.00)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.534)(0.10,0.858)(0.15,0.818)(0.20,0.82)(0.25,0.816)(0.30,0.866)(0.35,0.898)(0.40,0.84)(0.45,0.894)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.152)(0.10,0.334)(0.15,0.376)(0.20,0.424)(0.25,0.422)(0.30,0.442)(0.35,0.444)(0.40,0.582)(0.45,0.616)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.18)(0.10,0.378)(0.15,0.318)(0.20,0.392)(0.25,0.378)(0.30,0.35)(0.35,0.394)(0.40,0.64)(0.45,0.542)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.55)(0.10,0.622)(0.15,0.638)(0.20,0.64)(0.25,0.644)(0.30,0.69)(0.35,0.75)(0.40,0.818)(0.45,0.934)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.284)(0.10,0.288)(0.15,0.304)(0.20,0.244)(0.25,0.338)(0.30,0.234)(0.35,0.324)(0.40,0.436)(0.45,0.438)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1.5,-4.8)(3.5,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(D)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.116)(0.20,0.182)(0.25,0.298)(0.30,0.47)(0.35,0.60)(0.40,0.846)(0.45,0.98)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.118)(0.15,0.16)(0.20,0.25)(0.25,0.35)(0.30,0.462)(0.35,0.616)(0.40,0.758)(0.45,0.896)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.062)(0.10,0.084)(0.15,0.10)(0.20,0.106)(0.25,0.124)(0.30,0.132)(0.35,0.23)(0.40,0.264)(0.45,0.606)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.082)(0.10,0.096)(0.15,0.118)(0.20,0.226)(0.25,0.134)(0.30,0.244)(0.35,0.162)(0.40,0.42)(0.45,0.514)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.076)(0.10,0.10)(0.15,0.10)(0.20,0.10)(0.25,0.106)(0.30,0.258)(0.35,0.61)(0.40,0.884)(0.45,0.978)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.062)(0.10,0.10)(0.15,0.10)(0.20,0.102)(0.25,0.148)(0.30,0.278)(0.35,0.446)(0.40,0.722)(0.45,0.814)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.10,0.098)(0.10,0.10)(0.15,0.10)(0.20,0.102)(0.25,0.104)(0.30,0.102)(0.35,0.136)(0.40,0.232)(0.45,0.43)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.09)(0.10,0.10)(0.15,0.104)(0.20,0.11)(0.25,0.104)(0.30,0.132)(0.35,0.156)(0.40,0.19)(0.45,0.332)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.108)(0.15,0.126)(0.20,0.182)(0.25,0.262)(0.30,0.346)(0.35,0.544)(0.40,0.62)(0.45,0.784)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.106)(0.15,0.12)(0.20,0.112)(0.25,0.126)(0.30,0.17)(0.35,0.17)(0.40,0.202)(0.45,0.16)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1.5,-4.8)(3.5,5)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(E)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
%
\psset{origin={-0.05,-0.3}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.316)(0.10,0.498)(0.15,0.568)(0.20,0.724)(0.25,0.892)(0.30,0.954)(0.35,0.978)(0.40,0.994)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.454)(0.10,0.542)(0.15,0.646)(0.20,0.748)(0.25,0.836)(0.30,0.866)(0.35,0.918)(0.40,0.958)(0.45,0.976)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.334)(0.10,0.476)(0.15,0.504)(0.20,0.546)(0.25,0.644)(0.30,0.748)(0.35,0.836)(0.40,0.922)(0.45,0.982)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.452)(0.10,0.516)(0.15,0.548)(0.20,0.582)(0.25,0.666)(0.30,0.736)(0.35,0.812)(0.40,0.892)(0.45,0.928)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.51)(0.20,0.544)(0.25,0.606)(0.30,0.736)(0.35,0.902)(0.40,0.978)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.516)(0.20,0.55)(0.25,0.622)(0.30,0.726)(0.35,0.808)(0.40,0.944)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.498)(0.10,0.50)(0.15,0.502)(0.20,0.51)(0.25,0.54)(0.30,0.672)(0.35,0.806)(0.40,0.92)(0.45,0.976)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.496)(0.10,0.50)(0.15,0.51)(0.20,0.518)(0.25,0.54)(0.30,0.618)(0.35,0.696)(0.40,0.862)(0.45,0.892)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.336)(0.10,0.36)(0.15,0.388)(0.20,0.446)(0.25,0.536)(0.30,0.678)(0.35,0.856)(0.40,0.938)(0.45,0.972)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.51)(0.15,0.528)(0.20,0.542)(0.25,0.552)(0.30,0.658)(0.35,0.716)(0.40,0.724)(0.45,0.822)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-4.8)(0.8,5)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(F)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
%
\psset{origin={-0.05,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.212)(0.15,0.322)(0.20,0.522)(0.25,0.784)(0.30,0.902)(0.35,0.97)(0.40,0.984)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.258)(0.15,0.384)(0.20,0.548)(0.25,0.702)(0.30,0.796)(0.35,0.872)(0.40,0.928)(0.45,0.966)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.198)(0.10,0.20)(0.15,0.206)(0.20,0.224)(0.25,0.30)(0.30,0.344)(0.35,0.40)(0.40,0.702)(0.45,0.838)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.204)(0.15,0.232)(0.20,0.226)(0.25,0.272)(0.30,0.416)(0.35,0.442)(0.40,0.626)(0.45,0.754)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.212)(0.20,0.272)(0.25,0.376)(0.30,0.602)(0.35,0.84)(0.40,0.962)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.218)(0.20,0.268)(0.25,0.378)(0.30,0.54)(0.35,0.65)(0.40,0.884)(0.45,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.204)(0.25,0.218)(0.30,0.24)(0.35,0.286)(0.40,0.518)(0.45,0.882)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.218)(0.25,0.218)(0.30,0.246)(0.35,0.312)(0.40,0.486)(0.45,0.646)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.228)(0.15,0.27)(0.20,0.34)(0.25,0.454)(0.30,0.564)(0.35,0.762)(0.40,0.848)(0.45,0.942)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.206)(0.15,0.204)(0.20,0.204)(0.25,0.248)(0.30,0.244)(0.35,0.338)(0.40,0.35)(0.45,0.364)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%
\vspace*{-0.5in}
\caption{\label{newfig2}Effect of variations of equity to asset ratio (with respect to shock) on the vulnerability index $\xi$ for 
$(\alpha,\beta)$-heterogeneous networks. Lower values of $\xi$ imply higher global stability of a network.
}
%
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
























\clearpage
%%%%\thispagestyle{empty}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig3
%%\input{../tex-figures/newfig3-coordinated-only.tex}

\begin{figure*}
%
\vspace*{1.0in}
%
%%\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.7}[0.5]{
\begin{pspicture}(1.5,-6.2)(3.5,4.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(A)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.50)(0.46,1.50)
\rput[mr](0.70,1.55){\bf\normalsize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.50)(1.16,1.50)
\rput[mr](1.40,1.55){\bf\normalsize {\sf ER} model (average degree $3$), coordinated shock}
%%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.43)(0.46,1.43)
%%\rput[mr](0.7,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), random shock}
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](1.11,1.43)(1.16,1.43)
%%\rput[mr](1.40,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.41,1.36)(0.46,1.36)
\rput[mr](0.7,1.41){\bf\normalsize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](1.11,1.36)(1.16,1.36)
\rput[mr](1.40,1.41){\bf\normalsize {\sf SF} model (average degree $3$), coordinated shock}
%%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.41,1.29)(0.46,1.29)
%%\rput[mr](0.7,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), random shock}
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.29)(1.16,1.29)
%%\rput[mr](1.40,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.41,1.22)(0.46,1.22)
\rput[mr](0.70,1.27){\bf\normalsize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1.11,1.22)(1.16,1.22)
%%\rput[mr](1.40,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), random shock}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.649)(0.10,0.938)(0.15,0.984)(0.20,0.992)(0.25,0.995)(0.30,0.999)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.65)(0.10,0.86)(0.15,0.914)(0.20,0.928)(0.25,0.932)(0.30,0.941)(0.35,0.945)(0.40,0.946)(0.45,0.949)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.113)(0.10,0.235)(0.15,0.338)(0.20,0.35)(0.25,0.513)(0.30,0.668)(0.35,0.738)(0.40,0.684)(0.45,0.806)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.14)(0.10,0.161)(0.15,0.262)(0.20,0.282)(0.25,0.309)(0.30,0.389)(0.35,0.526)(0.40,0.466)(0.45,0.721)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.229)(0.10,0.708)(0.15,0.915)(0.20,0.968)(0.25,0.991)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.241)(0.10,0.629)(0.15,0.853)(0.20,0.888)(0.25,0.90)(0.30,0.90)(0.35,0.90)(0.40,0.90)(0.45,0.90)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.049)(0.10,0.086)(0.15,0.144)(0.20,0.186)(0.25,0.338)(0.30,0.363)(0.35,0.421)(0.40,0.324)(0.45,0.605)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.093)(0.10,0.101)(0.15,0.219)(0.20,0.18)(0.25,0.203)(0.30,0.225)(0.35,0.241)(0.40,0.29)(0.45,0.554)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.449)(0.10,0.676)(0.15,0.74)(0.20,0.787)(0.25,0.815)(0.30,0.839)(0.35,0.86)(0.40,0.888)(0.45,0.928)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.138)(0.10,0.171)(0.15,0.149)(0.20,0.163)(0.25,0.162)(0.30,0.25)(0.35,0.206)(0.40,0.196)(0.45,0.366)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{1in}
%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-7.4)(0.8,3.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(B)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,-0.3}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.701)(0.10,0.954)(0.15,0.991)(0.20,0.996)(0.25,0.996)(0.30,0.995)(0.35,0.993)(0.40,0.994)(0.45,0.995)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.77)(0.10,0.866)(0.15,0.892)(0.20,0.895)(0.25,0.894)(0.30,0.90)(0.35,0.905)(0.40,0.928)(0.45,0.955)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.525)(0.10,0.697)(0.15,0.755)(0.20,0.799)(0.25,0.884)(0.30,0.91)(0.35,0.925)(0.40,0.934)(0.45,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.545)(0.10,0.678)(0.15,0.658)(0.20,0.733)(0.25,0.772)(0.30,0.789)(0.35,0.818)(0.40,0.861)(0.45,0.911)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.284)(0.10,0.901)(0.15,0.968)(0.20,0.988)(0.25,0.995)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.488)(0.10,0.828)(0.15,0.947)(0.20,0.947)(0.25,0.947)(0.30,0.947)(0.35,0.948)(0.40,0.948)(0.45,0.948)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.31)(0.10,0.581)(0.15,0.73)(0.20,0.819)(0.25,0.83)(0.30,0.928)(0.35,0.975)(0.40,0.966)(0.45,0.984)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.442)(0.10,0.61)(0.15,0.681)(0.20,0.781)(0.25,0.788)(0.30,0.784)(0.35,0.804)(0.40,0.894)(0.45,0.934)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.529)(0.10,0.608)(0.15,0.608)(0.20,0.608)(0.25,0.609)(0.30,0.73)(0.35,0.809)(0.40,0.904)(0.45,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.598)(0.10,0.665)(0.15,0.638)(0.20,0.671)(0.25,0.621)(0.30,0.701)(0.35,0.767)(0.40,0.738)(0.45,0.827)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-7.2)(0.8,3.6)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(C)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.832)(0.10,0.984)(0.15,0.994)(0.20,0.998)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.768)(0.10,0.895)(0.15,0.915)(0.20,0.93)(0.25,0.931)(0.30,0.934)(0.35,0.936)(0.40,0.933)(0.45,0.933)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.241)(0.10,0.442)(0.15,0.614)(0.20,0.522)(0.25,0.768)(0.30,0.69)(0.35,0.871)(0.40,0.80)(0.45,0.909)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.28)(0.10,0.317)(0.15,0.435)(0.20,0.655)(0.25,0.549)(0.30,0.616)(0.35,0.629)(0.40,0.688)(0.45,0.822)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.521)(0.10,0.925)(0.15,0.968)(0.20,0.997)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.473)(0.10,0.825)(0.15,0.914)(0.20,0.916)(0.25,0.916)(0.30,0.916)(0.35,0.917)(0.40,0.917)(0.45,0.917)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.17)(0.10,0.236)(0.15,0.476)(0.20,0.57)(0.25,0.593)(0.30,0.626)(0.35,0.642)(0.40,0.74)(0.45,0.887)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.201)(0.10,0.415)(0.15,0.399)(0.20,0.448)(0.25,0.315)(0.30,0.437)(0.35,0.529)(0.40,0.598)(0.45,0.693)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.489)(0.10,0.626)(0.15,0.641)(0.20,0.646)(0.25,0.651)(0.30,0.70)(0.35,0.755)(0.40,0.84)(0.45,0.922)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.267)(0.10,0.27)(0.15,0.375)(0.20,0.241)(0.25,0.401)(0.30,0.372)(0.35,0.374)(0.40,0.476)(0.45,0.447)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-7.2)(3.5,2.6)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(D)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.79)(0.10,0.97)(0.15,0.99)(0.20,0.995)(0.25,0.996)(0.30,0.996)(0.35,0.997)(0.40,0.997)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.63)(0.10,0.77)(0.15,0.81)(0.20,0.84)(0.25,0.93)(0.30,0.94)(0.35,0.94)(0.40,0.94)(0.45,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.18)(0.10,0.25)(0.15,0.36)(0.20,0.47)(0.25,0.52)(0.30,0.63)(0.35,0.84)(0.40,0.84)(0.45,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.16)(0.10,0.24)(0.15,0.32)(0.20,0.36)(0.25,0.40)(0.30,0.52)(0.35,0.64)(0.40,0.64)(0.45,0.63)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.15)(0.10,0.38)(0.15,0.72)(0.20,0.90)(0.25,0.96)(0.30,0.98)(0.35,0.996)(0.40,0.996)(0.45,0.996)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.30)(0.15,0.56)(0.20,0.75)(0.25,0.88)(0.30,0.88)(0.35,0.88)(0.40,0.88)(0.45,0.88)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.06)(0.10,0.08)(0.15,0.11)(0.20,0.18)(0.25,0.25)(0.30,0.35)(0.35,0.51)(0.40,0.68)(0.45,0.80)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.09)(0.10,0.09)(0.15,0.14)(0.20,0.18)(0.25,0.33)(0.30,0.24)(0.35,0.35)(0.40,0.51)(0.45,0.74)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.69)(0.15,0.77)(0.20,0.80)(0.25,0.83)(0.30,0.84)(0.35,0.86)(0.40,0.88)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.15)(0.10,0.16)(0.15,0.17)(0.20,0.18)(0.25,0.16)(0.30,0.18)(0.35,0.23)(0.40,0.19)(0.45,0.25)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-10.2)(3.5,-0.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(E)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.3}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.88)(0.10,0.98)(0.15,0.99)(0.20,0.99)(0.25,0.99)(0.30,0.99)(0.35,0.99)(0.40,0.99)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.71)(0.10,0.78)(0.15,0.87)(0.20,0.87)(0.25,0.87)(0.30,0.87)(0.35,0.88)(0.40,0.92)(0.45,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.63)(0.10,0.78)(0.15,0.86)(0.20,0.90)(0.25,0.92)(0.30,0.93)(0.35,0.92)(0.40,0.94)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.56)(0.10,0.69)(0.15,0.73)(0.20,0.73)(0.25,0.76)(0.30,0.76)(0.35,0.80)(0.40,0.86)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.37)(0.10,0.69)(0.15,0.88)(0.20,0.96)(0.25,0.98)(0.30,0.99)(0.35,0.997)(0.40,0.997)(0.45,0.997)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.64)(0.15,0.80)(0.20,0.89)(0.25,0.93)(0.30,0.93)(0.35,0.93)(0.40,0.93)(0.45,0.93)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.34)(0.10,0.50)(0.15,0.64)(0.20,0.85)(0.25,0.90)(0.30,0.95)(0.35,0.96)(0.40,0.96)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.45)(0.10,0.54)(0.15,0.62)(0.20,0.78)(0.25,0.84)(0.30,0.89)(0.35,0.89)(0.40,0.90)(0.45,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.55)(0.10,0.63)(0.15,0.63)(0.20,0.63)(0.25,0.63)(0.30,0.76)(0.35,0.84)(0.40,0.92)(0.45,0.98)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.60)(0.10,0.64)(0.15,0.64)(0.20,0.64)(0.25,0.64)(0.30,0.71)(0.35,0.74)(0.40,0.76)(0.45,0.80)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-8.8)(0.8,1)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(F)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.88)(0.10,0.98)(0.15,0.99)(0.20,0.99)(0.25,0.995)(0.30,0.996)(0.35,0.997)(0.40,0.996)(0.45,0.993)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.69)(0.10,0.79)(0.15,0.81)(0.20,0.82)(0.25,0.91)(0.30,0.92)(0.35,0.92)(0.40,0.92)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.33)(0.10,0.47)(0.15,0.64)(0.20,0.74)(0.25,0.79)(0.30,0.81)(0.35,0.91)(0.40,0.88)(0.45,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.29)(0.10,0.40)(0.15,0.49)(0.20,0.60)(0.25,0.66)(0.30,0.71)(0.35,0.69)(0.40,0.69)(0.45,0.82)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.28)(0.10,0.59)(0.15,0.85)(0.20,0.96)(0.25,0.97)(0.30,0.997)(0.35,0.997)(0.40,0.997)(0.45,0.997)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.26)(0.10,0.46)(0.15,0.64)(0.20,0.86)(0.25,0.89)(0.30,0.89)(0.35,0.89)(0.40,0.89)(0.45,0.89)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.19)(0.10,0.24)(0.15,0.23)(0.20,0.27)(0.25,0.64)(0.30,0.72)(0.35,0.85)(0.40,0.90)(0.45,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.23)(0.15,0.26)(0.20,0.34)(0.25,0.50)(0.30,0.54)(0.35,0.69)(0.40,0.79)(0.45,0.81)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.62)(0.15,0.66)(0.20,0.67)(0.25,0.68)(0.30,0.72)(0.35,0.77)(0.40,0.85)(0.45,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.26)(0.10,0.29)(0.15,0.32)(0.20,0.33)(0.25,0.29)(0.30,0.34)(0.35,0.42)(0.40,0.44)(0.45,0.45)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 7 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-9.2)(3.5,1.2)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(G)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.105)(0.15,0.136)(0.20,0.21)(0.25,0.331)(0.30,0.471)(0.35,0.632)(0.40,0.854)(0.45,0.958)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.101)(0.10,0.124)(0.15,0.181)(0.20,0.261)(0.25,0.384)(0.30,0.469)(0.35,0.588)(0.40,0.756)(0.45,0.867)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.092)(0.10,0.10)(0.15,0.105)(0.20,0.109)(0.25,0.137)(0.30,0.163)(0.35,0.223)(0.40,0.396)(0.45,0.659)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.097)(0.10,0.101)(0.15,0.19)(0.20,0.124)(0.25,0.143)(0.30,0.275)(0.35,0.344)(0.40,0.376)(0.45,0.63)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.101)(0.20,0.108)(0.25,0.143)(0.30,0.241)(0.35,0.449)(0.40,0.719)(0.45,0.863)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.098)(0.10,0.10)(0.15,0.105)(0.20,0.119)(0.25,0.149)(0.30,0.216)(0.35,0.341)(0.40,0.543)(0.45,0.797)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.10)(0.20,0.10)(0.25,0.106)(0.30,0.106)(0.35,0.126)(0.40,0.208)(0.45,0.126)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.098)(0.10,0.10)(0.15,0.10)(0.20,0.102)(0.25,0.107)(0.30,0.11)(0.35,0.147)(0.40,0.244)(0.45,0.473)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.113)(0.15,0.143)(0.20,0.177)(0.25,0.244)(0.30,0.356)(0.35,0.437)(0.40,0.596)(0.45,0.769)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.103)(0.15,0.104)(0.20,0.106)(0.25,0.117)(0.30,0.14)(0.35,0.158)(0.40,0.183)(0.45,0.253)
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 8 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-13.2)(3.5,-3.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(H)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.3}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.493)(0.10,0.512)(0.15,0.589)(0.20,0.762)(0.25,0.898)(0.30,0.966)(0.35,0.982)(0.40,0.991)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.502)(0.10,0.536)(0.15,0.619)(0.20,0.746)(0.25,0.805)(0.30,0.861)(0.35,0.912)(0.40,0.937)(0.45,0.958)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.489)(0.10,0.501)(0.15,0.525)(0.20,0.569)(0.25,0.683)(0.30,0.747)(0.35,0.868)(0.40,0.938)(0.45,0.986)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.51)(0.15,0.54)(0.20,0.586)(0.25,0.679)(0.30,0.724)(0.35,0.785)(0.40,0.869)(0.45,0.922)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.501)(0.20,0.512)(0.25,0.542)(0.30,0.615)(0.35,0.742)(0.40,0.893)(0.45,0.976)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.505)(0.20,0.518)(0.25,0.543)(0.30,0.601)(0.35,0.689)(0.40,0.811)(0.45,0.938)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.507)(0.20,0.521)(0.25,0.544)(0.30,0.578)(0.35,0.756)(0.40,0.89)(0.45,0.756)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.504)(0.15,0.51)(0.20,0.527)(0.25,0.556)(0.30,0.596)(0.35,0.703)(0.40,0.788)(0.45,0.903)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.347)(0.10,0.364)(0.15,0.39)(0.20,0.435)(0.25,0.494)(0.30,0.669)(0.35,0.777)(0.40,0.905)(0.45,0.971)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.506)(0.15,0.519)(0.20,0.535)(0.25,0.567)(0.30,0.637)(0.35,0.656)(0.40,0.706)(0.45,0.773)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 9 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-10.8)(0.8,-1)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(I)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.201)(0.10,0.217)(0.15,0.329)(0.20,0.563)(0.25,0.772)(0.30,0.902)(0.35,0.965)(0.40,0.982)(0.45,0.995)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.202)(0.10,0.253)(0.15,0.386)(0.20,0.543)(0.25,0.674)(0.30,0.771)(0.35,0.862)(0.40,0.919)(0.45,0.952)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.201)(0.15,0.207)(0.20,0.228)(0.25,0.277)(0.30,0.352)(0.35,0.524)(0.40,0.692)(0.45,0.836)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.208)(0.15,0.224)(0.20,0.255)(0.25,0.373)(0.30,0.412)(0.35,0.465)(0.40,0.606)(0.45,0.726)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.203)(0.20,0.216)(0.25,0.262)(0.30,0.366)(0.35,0.583)(0.40,0.824)(0.45,0.961)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.206)(0.20,0.22)(0.25,0.254)(0.30,0.319)(0.35,0.456)(0.40,0.644)(0.45,0.884)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.207)(0.25,0.227)(0.30,0.241)(0.35,0.31)(0.40,0.533)(0.45,0.31)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.203)(0.20,0.21)(0.25,0.218)(0.30,0.238)(0.35,0.318)(0.40,0.476)(0.45,0.73)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.219)(0.15,0.262)(0.20,0.312)(0.25,0.399)(0.30,0.519)(0.35,0.626)(0.40,0.789)(0.45,0.926)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.204)(0.15,0.21)(0.20,0.219)(0.25,0.234)(0.30,0.277)(0.35,0.334)(0.40,0.373)(0.45,0.394)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 10 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-11)(3.5,-0.6)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(J)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.11)(0.15,0.14)(0.20,0.22)(0.25,0.36)(0.30,0.49)(0.35,0.65)(0.40,0.85)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.12)(0.15,0.18)(0.20,0.26)(0.25,0.36)(0.30,0.46)(0.35,0.58)(0.40,0.72)(0.45,0.86)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.101)(0.20,0.112)(0.25,0.141)(0.30,0.165)(0.35,0.224)(0.40,0.355)(0.45,0.632)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.184)(0.15,0.111)(0.20,0.20)(0.25,0.144)(0.30,0.24)(0.35,0.30)(0.40,0.397)(0.45,0.582)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.10)(0.20,0.105)(0.25,0.11)(0.30,0.129)(0.35,0.163)(0.40,0.264)(0.45,0.649)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.102)(0.20,0.106)(0.25,0.116)(0.30,0.132)(0.35,0.161)(0.40,0.239)(0.45,0.536)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.102)(0.20,0.107)(0.25,0.114)(0.30,0.118)(0.35,0.121)(0.40,0.165)(0.45,0.629)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.102)(0.20,0.106)(0.25,0.109)(0.30,0.117)(0.35,0.136)(0.40,0.183)(0.45,0.478)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.112)(0.15,0.133)(0.20,0.186)(0.25,0.258)(0.30,0.35)(0.35,0.434)(0.40,0.566)(0.45,0.778)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.102)(0.15,0.108)(0.20,0.112)(0.25,0.12)(0.30,0.141)(0.35,0.163)(0.40,0.182)(0.45,0.21)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 11 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-16.2)(3.5,-6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(K)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.3}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.52)(0.15,0.63)(0.20,0.796)(0.25,0.906)(0.30,0.952)(0.35,0.982)(0.40,0.993)(0.45,0.999)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.502)(0.10,0.554)(0.15,0.646)(0.20,0.749)(0.25,0.818)(0.30,0.869)(0.35,0.907)(0.40,0.94)(0.45,0.966)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.502)(0.15,0.529)(0.20,0.615)(0.25,0.701)(0.30,0.765)(0.35,0.85)(0.40,0.921)(0.45,0.978)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.514)(0.15,0.553)(0.20,0.611)(0.25,0.661)(0.30,0.745)(0.35,0.792)(0.40,0.866)(0.45,0.925)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.50)(0.20,0.504)(0.25,0.507)(0.30,0.52)(0.35,0.543)(0.40,0.613)(0.45,0.857)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.502)(0.20,0.505)(0.25,0.513)(0.30,0.522)(0.35,0.547)(0.40,0.607)(0.45,0.797)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.501)(0.10,0.507)(0.15,0.511)(0.20,0.514)(0.25,0.535)(0.30,0.62)(0.35,0.678)(0.40,0.82)(0.45,0.903)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.502)(0.10,0.508)(0.15,0.51)(0.20,0.513)(0.25,0.542)(0.30,0.57)(0.35,0.69)(0.40,0.767)(0.45,0.81)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.331)(0.10,0.351)(0.15,0.376)(0.20,0.444)(0.25,0.505)(0.30,0.667)(0.35,0.776)(0.40,0.882)(0.45,0.972)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.507)(0.15,0.515)(0.20,0.539)(0.25,0.57)(0.30,0.62)(0.35,0.666)(0.40,0.706)(0.45,0.761)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 12 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-12.8)(0.8,-3)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(L)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.225)(0.15,0.36)(0.20,0.572)(0.25,0.77)(0.30,0.891)(0.35,0.953)(0.40,0.987)(0.45,0.997)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.202)(0.10,0.266)(0.15,0.39)(0.20,0.544)(0.25,0.664)(0.30,0.763)(0.35,0.838)(0.40,0.889)(0.45,0.927)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.211)(0.20,0.235)(0.25,0.284)(0.30,0.371)(0.35,0.482)(0.40,0.676)(0.45,0.858)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.274)(0.15,0.278)(0.20,0.254)(0.25,0.344)(0.30,0.39)(0.35,0.485)(0.40,0.622)(0.45,0.743)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.205)(0.25,0.211)(0.30,0.23)(0.35,0.265)(0.40,0.368)(0.45,0.756)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.202)(0.20,0.206)(0.25,0.216)(0.30,0.232)(0.35,0.262)(0.40,0.341)(0.45,0.628)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.202)(0.15,0.21)(0.20,0.214)(0.25,0.217)(0.30,0.23)(0.35,0.294)(0.40,0.567)(0.45,0.816)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.202)(0.15,0.207)(0.20,0.213)(0.25,0.215)(0.30,0.226)(0.35,0.277)(0.40,0.472)(0.45,0.70)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.225)(0.15,0.26)(0.20,0.337)(0.25,0.417)(0.30,0.536)(0.35,0.642)(0.40,0.781)(0.45,0.93)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.206)(0.15,0.209)(0.20,0.226)(0.25,0.241)(0.30,0.282)(0.35,0.325)(0.40,0.321)(0.45,0.393)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
\vspace*{-2.0in}
\caption{\label{newfig3}Effect of variations of equity to asset ratio (with respect to shock) on the vulnerability index $\xi$ for 
$(\alpha,\beta)$-heterogeneous networks. Lower values of $\xi$ imply higher global stability of a network.
}
%
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%























\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig4 
%%\input{../tex-figures/newfig4-coordinated-only.tex}

\begin{figure*}
%
\vspace*{1.2in}
%%\hspace*{-0.0in}
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-3,-7.5)(-1,9.5)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}
%
%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[mr](5,-7.5){\LARGE\bf (A)}
%
\psline[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](7.50,16.2)(8.5,16.2)
\rput[mr](7.35,16.2){\LARGE\bf {\sf ER} model (average degree $\pmb{6}$), coordinated shock}
\psline[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](24.65,16.2)(25.65,16.2)
\rput[mr](24.55,16.2){\LARGE\bf {\sf ER} model (average degree $\pmb{3}$), coordinated shock}
%%
%%\psline[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](17.20,15.3)(18.20,15.3)
%%\rput[mr](17.05,15.3){\Large\bf {\sf ER} model (average degree $\pmb{6}$), random shock}
%%\psline[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](31.55,15.3)(32.55,15.3)
%%\rput[mr](31.05,15.3){\Large\bf {\sf ER} model (average degree $\pmb{3}$), random shock}
%%
\psline[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](7.50,14.4)(8.5,14.4)
\rput[mr](7.35,14.4){\LARGE\bf {\sf SF} model (average degree $\pmb{6}$), coordinated shock}
\psline[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](24.65,14.4)(25.65,14.4)
\rput[mr](24.55,14.4){\LARGE\bf {\sf SF} model (average degree $\pmb{3}$), coordinated shock}
%%
%%\psline[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](17.20,13.5)(18.20,13.5)
%%\rput[mr](17.05,13.3){\Large\bf {\sf SF} model (average degree $\pmb{6}$), random shock}
%%\psline[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](31.55,13.5)(32.55,13.5)
%%\rput[mr](31.05,13.5){\Large\bf {\sf SF} model (average degree $\pmb{3}$), random shock}
%%
\psline[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](10,12.5)(11,12.5)
\rput[mr](9.85,12.5){\LARGE\bf in-arborescence (average degree $\pmb{\approx 1}$), coordinated shock}
%%
%%\psline[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](25.95,12.5)(26.95,12.5)
%%\rput[mr](25.85,12.5){\Large\bf in-arborescence (average degree $\pmb{\approx 1}$), random shock}
%
\rput[ml](1,11.0){\Large$\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,01.06)(1,2,01.06)(1,3,01.06)(1,4,01.36)(1,5,01.36)(1,6,01.36)(1,7,01.36)(1,8,01.64)(1,9,01.64)(1,10,01.64)(1,11,01.64)(1,12,01.88)(1,13,01.88)(1,14,01.88)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.14)(5,2,00.14)(5,3,00.14)(5,4,00.2)(5,5,00.2)(5,6,00.2)(5,7,00.2)(5,8,00.3)(5,9,00.3)(5,10,00.3)(5,11,00.3)(5,12,00.3)(5,13,00.3)(5,14,00.3)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.02)(9,2,00.02)(9,3,00.02)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,02.9)(1,2,02.9)(1,3,02.9)(1,4,03.14)(1,5,03.14)(1,6,03.14)(1,7,03.14)(1,8,03.62)(1,9,03.62)(1,10,03.62)(1,11,03.62)(1,12,04.02)(1,13,04.02)(1,14,04.02)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,00.58)(5,2,00.58)(5,3,00.58)(5,4,00.4)(5,5,00.4)(5,6,00.4)(5,7,00.4)(5,8,00.52)(5,9,00.52)(5,10,00.52)(5,11,00.52)(5,12,00.58)(5,13,00.58)(5,14,00.58)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.34)(9,2,00.34)(9,3,00.34)(9,4,00.04)(9,5,00.04)(9,6,00.04)(9,7,00.04)(9,8,00.04)(9,9,00.04)(9,10,00.04)(9,11,00.04)(9,12,00.04)(9,13,00.04)(9,14,00.04)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,01.82)(1,2,01.76)(1,3,01.12)(1,4,01.18)(1,5,03.56)(1,6,01.86)(1,7,02.84)(1,8,04.3)(1,9,02.0)(1,10,02.88)(1,11,02.16)(1,12,03.96)(1,13,03.56)(1,14,04.66)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.06)(5,2,00.12)(5,3,00.18)(5,4,00.14)(5,5,00.16)(5,6,00.12)(5,7,00.22)(5,8,00.2)(5,9,00.24)(5,10,00.36)(5,11,00.26)(5,12,00.38)(5,13,00.28)(5,14,00.36)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.02)(9,2,00.02)(9,3,00.02)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,06.8)(1,2,05.72)(1,3,04.44)(1,4,06.76)(1,5,04.66)(1,6,04.12)(1,7,06.28)(1,8,08.18)(1,9,0.624)(1,10,07.04)(1,11,05.3)(1,12,06.32)(1,13,06.84)(1,14,07.28)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,00.5)(5,2,00.42)(5,3,00.56)(5,4,00.26)(5,5,00.38)(5,6,00.44)(5,7,00.34)(5,8,01.44)(5,9,00.52)(5,10,00.42)(5,11,01.5)(5,12,00.54)(5,13,00.62)(5,14,00.6)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.34)(9,2,00.34)(9,3,00.36)(9,4,00.06)(9,5,00.02)(9,6,00.02)(9,7,00.02)(9,8,00.02)(9,9,00.04)(9,10,00.08)(9,11,00.04)(9,12,00.02)(9,13,00.1)(9,14,00.04)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,07.22)(1,2,07.22)(1,3,07.22)(1,4,06.92)(1,5,06.92)(1,6,06.92)(1,7,06.92)(1,8,06.66)(1,9,06.66)(1,10,06.66)(1,11,06.66)(1,12,06.48)(1,13,06.48)(1,14,06.48)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.06)(5,2,00.06)(5,3,00.06)(5,4,00.04)(5,5,00.04)(5,6,00.04)(5,7,00.04)(5,8,00.06)(5,9,00.06)(5,10,00.06)(5,11,00.06)(5,12,00.06)(5,13,00.06)(5,14,00.06)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.02)(9,2,00.02)(9,3,00.02)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,08.84)(1,2,08.84)(1,3,08.84)(1,4,08.54)(1,5,08.54)(1,6,08.54)(1,7,08.54)(1,8,08.02)(1,9,08.02)(1,10,08.02)(1,11,08.02)(1,12,07.14)(1,13,07.14)(1,14,07.14)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,01.14)(5,2,01.14)(5,3,01.14)(5,4,00.26)(5,5,00.26)(5,6,00.26)(5,7,00.26)(5,8,00.18)(5,9,00.18)(5,10,00.18)(5,11,00.18)(5,12,00.22)(5,13,00.22)(5,14,00.22)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,00.72)(9,2,00.72)(9,3,00.72)(9,4,00.06)(9,5,00.06)(9,6,00.06)(9,7,00.06)(9,8,00.06)(9,9,00.06)(9,10,00.06)(9,11,00.06)(9,12,00.06)(9,13,00.06)(9,14,00.06)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,02.28)(1,2,01.4)(1,3,01.46)(1,4,01.52)(1,5,00.7)(1,6,02.54)(1,7,01.72)(1,8,01.84)(1,9,01.76)(1,10,00.72)(1,11,01.82)(1,12,02.88)(1,13,02.88)(1,14,00.94)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,00.14)(5,2,00.14)(5,3,00.18)(5,4,00.2)(5,5,00.16)(5,6,00.18)(5,7,00.22)(5,8,00.36)(5,9,00.36)(5,10,00.36)(5,11,00.3)(5,12,00.5)(5,13,00.4)(5,14,00.4)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.002)(9,3,0.002)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,03.26)(1,2,01.92)(1,3,02.22)(1,4,02.46)(1,5,04.66)(1,6,02.52)(1,7,02.96)(1,8,03.26)(1,9,03.18)(1,10,02.7)(1,11,04.68)(1,12,02.86)(1,13,04.14)(1,14,04.3)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,01.02)(5,2,00.8)(5,3,00.96)(5,4,00.42)(5,5,00.3)(5,6,00.48)(5,7,00.42)(5,8,00.56)(5,9,00.6)(5,10,00.54)(5,11,00.46)(5,12,00.8)(5,13,00.66)(5,14,00.68)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.66)(9,2,00.68)(9,3,00.74)(9,4,00.02)(9,5,00.04)(9,6,00.08)(9,7,00.1)(9,8,00.04)(9,9,00.16)(9,10,00.06)(9,11,00.16)(9,12,00.06)(9,13,00.08)(9,14,00.08)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,09.38)(1,2,09.38)(1,3,09.38)(1,4,07.4)(1,5,07.4)(1,6,07.4)(1,7,07.4)(1,8,06.96)(1,9,06.96)(1,10,06.96)(1,11,06.96)(1,12,06.78)(1,13,06.78)(1,14,06.78)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,07.58)(5,2,07.58)(5,3,07.58)(5,4,01.84)(5,5,01.84)(5,6,01.84)(5,7,01.84)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,06.62)(9,2,06.62)(9,3,06.62)(9,4,00.3)(9,5,00.3)(9,6,00.3)(9,7,00.3)(9,8,00.3)(9,9,00.3)(9,10,00.3)(9,11,00.3)(9,12,00.34)(9,13,00.34)(9,14,00.34)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,06.32)(1,2,06.58)(1,3,06.52)(1,4,01.2)(1,5,01.4)(1,6,01.74)(1,7,01.74)(1,8,02.78)(1,9,02.18)(1,10,02.66)(1,11,02.62)(1,12,02.08)(1,13,02.26)(1,14,02.66)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,06.12)(5,2,05.84)(5,3,05.78)(5,4,00.26)(5,5,00.36)(5,6,00.68)(5,7,00.48)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,05.8)(9,2,05.68)(9,3,05.74)(9,4,00.04)(9,5,00.04)(9,6,00.0)(9,7,00.0)(9,8,00.02)(9,9,00.06)(9,10,00.0)(9,11,00.0)(9,12,00.02)(9,13,00.02)(9,14,00.06)
%
%\pstThreeDPut(1,1,8){haha}
%
%%\savedata{\mydata}[
%%{
%%(1,1,0.00)(1,2,0.02)(1,3,0.06)(1,4,0.12)(1,5,0.2)(1,6,0.3)(1,7,0.34)(1,8,0.56)(1,9,1.36)
%%%(2,1,0.00)(2,2,0.02)(2,3,0.06)(2,4,0.12)(2,5,0.2)(2,6,0.3)(2,7,0.34)(2,8,0.56)(2,9,1.36)
%%}
%%]
%%\dataplotThreeD[plotstyle=line,fillstyle=solid,fillcolor=red,gradbegin=red,gradmidpoint=0.5,linewidth=1pt]{\mydata}
%%%
%%\savedata{\mydata}[
%%{
%%(2,1,0.00)(2,2,0.02)(2,3,0.06)(2,4,0.12)(2,5,0.2)(2,6,0.3)(2,7,0.34)(2,8,0.56)(2,9,1.36)
%%}
%%]
%%\dataplotThreeD[plotstyle=line,fillstyle=solid,fillcolor=blue,gradbegin=red,gradmidpoint=0.5,linewidth=1pt]{\mydata}
%
%\savedata{\newdata}[{2,2,9}, {1,1,1}, {5,5,5}, {6,6,6}, {7,7,7}]
%\dataplotThreeD[plotstyle=curve,fillstyle=solid,fillcolor=blue,gradbegin=blue,gradmidpoint=0.5,linewidth=0pt]{\newdata}
%%%%%%%%%%%%%%%%%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%%%%%%%%%%%%%%%%%
\end{pspicture}
}
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% part 2 of figure starts
%
\hspace*{1.7in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-4,-7.5)(-2,9.5)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}

%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
\rput[ml](1,11.0){\Large$\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
\rput[mr](5,-7.5){\LARGE\bf (B)}
%
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,05.03)(1,2,05.03)(1,3,05.03)(1,4,06.70)(1,5,06.70)(1,6,06.70)(1,7,06.70)(1,8,07.90)(1,9,07.90)(1,10,07.90)(1,11,07.90)(1,12,09.00)(1,13,09.00)(1,14,09.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.80)(5,2,00.80)(5,3,00.80)(5,4,01.0)(5,5,01.0)(5,6,01.0)(5,7,01.0)(5,8,01.4)(5,9,01.4)(5,10,01.4)(5,11,01.4)(5,12,01.7)(5,13,01.7)(5,14,01.7)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,05.8)(1,2,05.8)(1,3,05.8)(1,4,07.50)(1,5,07.50)(1,6,07.50)(1,7,07.50)(1,8,08.70)(1,9,08.70)(1,10,08.70)(1,11,08.70)(1,12,09.20)(1,13,09.20)(1,14,09.20)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,01.60)(5,2,01.60)(5,3,01.60)(5,4,01.7)(5,5,01.7)(5,6,01.7)(5,7,01.7)(5,8,02.50)(5,9,02.50)(5,10,02.50)(5,11,02.50)(5,12,03.60)(5,13,03.60)(5,14,03.60)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.40)(9,2,00.40)(9,3,00.40)(9,4,00.10)(9,5,00.10)(9,6,00.10)(9,7,00.10)(9,8,00.10)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.20)(9,13,00.20)(9,14,00.20)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,07.20)(1,2,08.20)(1,3,04.60)(1,4,09.00)(1,5,07.80)(1,6,07.40)(1,7,07.20)(1,8,09.0)(1,9,08.8)(1,10,08.00)(1,11,08.60)(1,12,09.20)(1,13,08.60)(1,14,08.90)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.60)(5,2,00.60)(5,3,00.70)(5,4,00.80)(5,5,01.00)(5,6,00.80)(5,7,00.90)(5,8,01.3)(5,9,01.60)(5,10,01.40)(5,11,01.50)(5,12,01.90)(5,13,01.60)(5,14,02.00)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,06.7)(1,2,06.70)(1,3,07.60)(1,4,08.30)(1,5,07.20)(1,6,07.80)(1,7,08.10)(1,8,08.90)(1,9,9.000)(1,10,09.10)(1,11,08.8)(1,12,09.00)(1,13,09.00)(1,14,09.20)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,01.6)(5,2,01.40)(5,3,01.30)(5,4,01.80)(5,5,01.80)(5,6,02.60)(5,7,01.70)(5,8,02.60)(5,9,03.10)(5,10,02.50)(5,11,02.4)(5,12,03.20)(5,13,03.30)(5,14,03.7)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.50)(9,2,00.40)(9,3,00.40)(9,4,00.20)(9,5,00.20)(9,6,00.30)(9,7,00.30)(9,8,00.30)(9,9,00.30)(9,10,00.30)(9,11,00.20)(9,12,00.20)(9,13,00.2)(9,14,00.30)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,09.60)(1,2,09.60)(1,3,09.60)(1,4,07.80)(1,5,07.80)(1,6,07.80)(1,7,07.80)(1,8,08.40)(1,9,08.40)(1,10,08.40)(1,11,08.40)(1,12,08.10)(1,13,08.10)(1,14,08.10)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.60)(5,2,00.60)(5,3,00.60)(5,4,00.90)(5,5,00.90)(5,6,00.90)(5,7,00.90)(5,8,01.40)(5,9,01.40)(5,10,01.40)(5,11,01.40)(5,12,01.90)(5,13,01.90)(5,14,01.90)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,08.60)(1,2,08.60)(1,3,08.60)(1,4,08.70)(1,5,08.70)(1,6,08.70)(1,7,08.70)(1,8,08.70)(1,9,08.70)(1,10,08.70)(1,11,08.70)(1,12,08.70)(1,13,08.70)(1,14,08.70)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,02.60)(5,2,02.60)(5,3,02.60)(5,4,02.20)(5,5,02.20)(5,6,02.20)(5,7,02.20)(5,8,03.90)(5,9,03.90)(5,10,03.90)(5,11,03.90)(5,12,03.70)(5,13,03.70)(5,14,03.70)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,01.10)(9,2,01.10)(9,3,01.10)(9,4,00.40)(9,5,00.40)(9,6,00.40)(9,7,00.40)(9,8,00.40)(9,9,00.40)(9,10,00.40)(9,11,00.40)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,08.00)(1,2,08.1)(1,3,06.70)(1,4,05.90)(1,5,05.9)(1,6,06.10)(1,7,07.00)(1,8,07.10)(1,9,07.10)(1,10,06.90)(1,11,06.90)(1,12,08.00)(1,13,08.30)(1,14,07.80)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,01.00)(5,2,00.80)(5,3,00.70)(5,4,01.2)(5,5,01.00)(5,6,01.30)(5,7,01.30)(5,8,01.70)(5,9,01.60)(5,10,01.70)(5,11,01.7)(5,12,02.2)(5,13,02.1)(5,14,02.2)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.000)(9,3,0.000)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,06.40)(1,2,07.40)(1,3,06.90)(1,4,07.60)(1,5,06.70)(1,6,07.90)(1,7,06.60)(1,8,08.10)(1,9,08.30)(1,10,08.8)(1,11,08.50)(1,12,08.80)(1,13,08.90)(1,14,08.7)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,02.20)(5,2,03.5)(5,3,02.30)(5,4,01.80)(5,5,02.1)(5,6,02.80)(5,7,02.00)(5,8,03.20)(5,9,03.4)(5,10,04.00)(5,11,03.90)(5,12,03.8)(5,13,03.80)(5,14,03.60)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.70)(9,2,00.70)(9,3,00.70)(9,4,00.30)(9,5,00.30)(9,6,00.50)(9,7,00.4)(9,8,00.30)(9,9,00.40)(9,10,00.30)(9,11,00.40)(9,12,00.30)(9,13,00.40)(9,14,00.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,10.00)(1,2,10.00)(1,3,10.00)(1,4,10.0)(1,5,10.0)(1,6,10.0)(1,7,10.0)(1,8,10.00)(1,9,10.00)(1,10,10.00)(1,11,10.00)(1,12,10.00)(1,13,10.00)(1,14,10.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,08.50)(5,2,08.50)(5,3,08.50)(5,4,04.50)(5,5,04.50)(5,6,04.50)(5,7,04.50)(5,8,03.7)(5,9,03.7)(5,10,03.7)(5,11,03.7)(5,12,03.7)(5,13,03.7)(5,14,03.7)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,06.60)(9,2,06.60)(9,3,06.60)(9,4,00.3)(9,5,00.3)(9,6,00.3)(9,7,00.3)(9,8,00.3)(9,9,00.3)(9,10,00.3)(9,11,00.3)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,05.80)(1,2,06.10)(1,3,05.80)(1,4,07.6)(1,5,06.8)(1,6,07.00)(1,7,07.30)(1,8,07.90)(1,9,08.30)(1,10,07.90)(1,11,08.20)(1,12,07.50)(1,13,08.70)(1,14,08.20)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,04.30)(5,2,04.10)(5,3,04.40)(5,4,02.10)(5,5,02.20)(5,6,02.50)(5,7,02.00)(5,8,05.0)(5,9,05.0)(5,10,05.0)(5,11,05.0)(5,12,05.0)(5,13,05.0)(5,14,05.0)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,03.4)(9,2,03.30)(9,3,03.30)(9,4,00.10)(9,5,00.20)(9,6,00.2)(9,7,00.1)(9,8,00.20)(9,9,00.20)(9,10,00.2)(9,11,00.2)(9,12,00.30)(9,13,00.20)(9,14,00.10)
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}
%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%
\end{pspicture}
}
%
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% part 3 of figure starts
%
\\
\hspace*{-0.0in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-3,-7)(-1.95,13)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}

%
%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
\rput[ml](1,11.0){\Large$\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
\rput[mr](5,-7.5){\LARGE\bf (C)}
%
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,01.20)(1,2,01.20)(1,3,01.20)(1,4,01.40)(1,5,01.40)(1,6,01.40)(1,7,01.40)(1,8,01.60)(1,9,01.60)(1,10,01.60)(1,11,01.60)(1,12,01.90)(1,13,01.90)(1,14,01.90)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.20)(5,2,00.20)(5,3,00.20)(5,4,00.2)(5,5,00.2)(5,6,00.2)(5,7,00.2)(5,8,00.3)(5,9,00.3)(5,10,00.3)(5,11,00.3)(5,12,00.3)(5,13,00.3)(5,14,00.3)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,02.3)(1,2,02.3)(1,3,02.3)(1,4,02.30)(1,5,02.30)(1,6,02.30)(1,7,02.30)(1,8,03.00)(1,9,03.00)(1,10,03.00)(1,11,03.00)(1,12,03.30)(1,13,03.30)(1,14,03.30)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,00.70)(5,2,00.70)(5,3,00.70)(5,4,00.4)(5,5,00.4)(5,6,00.4)(5,7,00.4)(5,8,00.50)(5,9,00.50)(5,10,00.50)(5,11,00.50)(5,12,00.60)(5,13,00.60)(5,14,00.60)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.50)(9,2,00.50)(9,3,00.50)(9,4,00.10)(9,5,00.10)(9,6,00.10)(9,7,00.10)(9,8,00.10)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.10)(9,13,00.10)(9,14,00.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,02.90)(1,2,01.00)(1,3,01.90)(1,4,01.50)(1,5,03.00)(1,6,02.20)(1,7,01.20)(1,8,02.9)(1,9,03.4)(1,10,02.40)(1,11,01.40)(1,12,03.30)(1,13,04.00)(1,14,03.00)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.10)(5,2,00.10)(5,3,00.10)(5,4,00.20)(5,5,00.20)(5,6,00.20)(5,7,00.20)(5,8,00.2)(5,9,00.30)(5,10,00.30)(5,11,00.30)(5,12,00.30)(5,13,00.40)(5,14,00.40)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,07.4)(1,2,08.10)(1,3,09.00)(1,4,06.80)(1,5,06.70)(1,6,05.90)(1,7,06.80)(1,8,05.80)(1,9,7.300)(1,10,07.20)(1,11,07.7)(1,12,08.20)(1,13,07.00)(1,14,07.90)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,00.7)(5,2,00.80)(5,3,00.60)(5,4,00.40)(5,5,00.30)(5,6,00.30)(5,7,00.40)(5,8,00.50)(5,9,00.40)(5,10,00.50)(5,11,00.5)(5,12,01.50)(5,13,00.60)(5,14,00.6)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.40)(9,2,00.50)(9,3,00.40)(9,4,00.00)(9,5,00.10)(9,6,00.00)(9,7,00.00)(9,8,00.00)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.10)(9,13,00.1)(9,14,00.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,09.60)(1,2,09.60)(1,3,09.60)(1,4,07.10)(1,5,07.10)(1,6,07.10)(1,7,07.10)(1,8,06.20)(1,9,06.20)(1,10,06.20)(1,11,06.20)(1,12,07.00)(1,13,07.00)(1,14,07.00)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.10)(5,2,00.10)(5,3,00.10)(5,4,00.10)(5,5,00.10)(5,6,00.10)(5,7,00.10)(5,8,00.10)(5,9,00.10)(5,10,00.10)(5,11,00.10)(5,12,00.10)(5,13,00.10)(5,14,00.10)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,07.60)(1,2,07.60)(1,3,07.60)(1,4,07.00)(1,5,07.00)(1,6,07.00)(1,7,07.00)(1,8,06.30)(1,9,06.30)(1,10,06.30)(1,11,06.30)(1,12,05.80)(1,13,05.80)(1,14,05.80)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,01.20)(5,2,01.20)(5,3,01.20)(5,4,00.40)(5,5,00.40)(5,6,00.40)(5,7,00.40)(5,8,00.30)(5,9,00.30)(5,10,00.30)(5,11,00.30)(5,12,00.30)(5,13,00.30)(5,14,00.30)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,00.90)(9,2,00.90)(9,3,00.90)(9,4,00.00)(9,5,00.00)(9,6,00.00)(9,7,00.00)(9,8,00.00)(9,9,00.00)(9,10,00.00)(9,11,00.00)(9,12,00.00)(9,13,00.00)(9,14,00.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,03.10)(1,2,04.2)(1,3,01.50)(1,4,03.40)(1,5,00.8)(1,6,01.60)(1,7,02.40)(1,8,01.70)(1,9,02.70)(1,10,02.40)(1,11,00.90)(1,12,01.00)(1,13,01.00)(1,14,01.10)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,00.20)(5,2,00.30)(5,3,00.20)(5,4,00.2)(5,5,00.30)(5,6,00.30)(5,7,00.30)(5,8,00.40)(5,9,00.40)(5,10,00.40)(5,11,00.4)(5,12,00.5)(5,13,00.5)(5,14,00.5)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.000)(9,3,0.000)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,02.70)(1,2,02.90)(1,3,03.90)(1,4,03.40)(1,5,03.80)(1,6,01.60)(1,7,03.50)(1,8,01.60)(1,9,04.10)(1,10,01.9)(1,11,02.60)(1,12,02.90)(1,13,01.90)(1,14,04.2)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,01.20)(5,2,01.0)(5,3,01.90)(5,4,00.50)(5,5,00.5)(5,6,00.60)(5,7,00.60)(5,8,01.20)(5,9,00.5)(5,10,00.60)(5,11,01.40)(5,12,00.9)(5,13,00.90)(5,14,00.80)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.90)(9,2,00.90)(9,3,00.80)(9,4,00.10)(9,5,00.10)(9,6,00.10)(9,7,00.1)(9,8,00.20)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.10)(9,13,00.10)(9,14,00.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,09.50)(1,2,09.50)(1,3,09.50)(1,4,07.6)(1,5,07.6)(1,6,07.6)(1,7,07.6)(1,8,07.40)(1,9,07.40)(1,10,07.40)(1,11,07.40)(1,12,07.00)(1,13,07.00)(1,14,07.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,07.60)(5,2,07.60)(5,3,07.60)(5,4,01.40)(5,5,01.40)(5,6,01.40)(5,7,01.40)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,07.00)(9,2,07.00)(9,3,07.00)(9,4,00.3)(9,5,00.3)(9,6,00.3)(9,7,00.3)(9,8,00.3)(9,9,00.3)(9,10,00.3)(9,11,00.3)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,06.40)(1,2,06.70)(1,3,06.80)(1,4,02.6)(1,5,01.8)(1,6,01.50)(1,7,02.10)(1,8,01.80)(1,9,02.40)(1,10,02.30)(1,11,02.50)(1,12,02.10)(1,13,02.40)(1,14,02.40)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,06.20)(5,2,06.30)(5,3,06.20)(5,4,00.40)(5,5,00.30)(5,6,00.40)(5,7,00.40)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,06.0)(9,2,06.10)(9,3,06.00)(9,4,00.00)(9,5,00.00)(9,6,00.0)(9,7,00.1)(9,8,00.00)(9,9,00.00)(9,10,00.1)(9,11,00.0)(9,12,00.00)(9,13,00.10)(9,14,00.10)
%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%
\end{pspicture}
}
%
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% part 4 of figure starts
%
\hspace*{1.7in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-4,-7.5)(-2,9.5)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}

%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
\rput[ml](1,11.0){\Large$\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
\rput[mr](5,-7.5){\LARGE\bf (D)}
%
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,04.80)(1,2,04.80)(1,3,04.80)(1,4,06.70)(1,5,06.70)(1,6,06.70)(1,7,06.70)(1,8,07.90)(1,9,07.90)(1,10,07.90)(1,11,07.90)(1,12,08.90)(1,13,08.90)(1,14,08.90)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.70)(5,2,00.70)(5,3,00.70)(5,4,01.1)(5,5,01.1)(5,6,01.1)(5,7,01.1)(5,8,01.5)(5,9,01.5)(5,10,01.5)(5,11,01.5)(5,12,01.8)(5,13,01.8)(5,14,01.8)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,06.3)(1,2,06.3)(1,3,06.3)(1,4,07.60)(1,5,07.60)(1,6,07.60)(1,7,07.60)(1,8,08.80)(1,9,08.80)(1,10,08.80)(1,11,08.80)(1,12,09.30)(1,13,09.30)(1,14,09.30)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,02.00)(5,2,02.00)(5,3,02.00)(5,4,02.2)(5,5,02.2)(5,6,02.2)(5,7,02.2)(5,8,02.70)(5,9,02.70)(5,10,02.70)(5,11,02.70)(5,12,03.20)(5,13,03.20)(5,14,03.20)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.70)(9,2,00.70)(9,3,00.70)(9,4,00.30)(9,5,00.30)(9,6,00.30)(9,7,00.30)(9,8,00.30)(9,9,00.30)(9,10,00.30)(9,11,00.30)(9,12,00.30)(9,13,00.30)(9,14,00.30)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,07.60)(1,2,08.00)(1,3,06.50)(1,4,06.90)(1,5,08.30)(1,6,08.50)(1,7,08.60)(1,8,08.7)(1,9,08.1)(1,10,08.40)(1,11,08.70)(1,12,09.10)(1,13,09.00)(1,14,09.20)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.70)(5,2,00.70)(5,3,00.70)(5,4,01.00)(5,5,01.00)(5,6,01.00)(5,7,01.20)(5,8,01.4)(5,9,01.40)(5,10,01.40)(5,11,01.30)(5,12,01.70)(5,13,01.80)(5,14,01.70)
%%\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,07.2)(1,2,07.30)(1,3,07.80)(1,4,08.40)(1,5,08.40)(1,6,07.80)(1,7,08.20)(1,8,08.60)(1,9,8.800)(1,10,09.00)(1,11,08.7)(1,12,09.20)(1,13,09.00)(1,14,09.00)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,01.7)(5,2,01.60)(5,3,02.40)(5,4,02.00)(5,5,01.90)(5,6,01.90)(5,7,01.90)(5,8,03.90)(5,9,02.50)(5,10,02.50)(5,11,04.0)(5,12,03.00)(5,13,04.40)(5,14,03.6)
%%\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.50)(9,2,00.60)(9,3,00.50)(9,4,00.30)(9,5,00.30)(9,6,00.30)(9,7,00.30)(9,8,00.30)(9,9,00.30)(9,10,00.30)(9,11,00.20)(9,12,00.30)(9,13,00.3)(9,14,00.30)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,09.40)(1,2,09.40)(1,3,09.40)(1,4,07.10)(1,5,07.10)(1,6,07.10)(1,7,07.10)(1,8,07.90)(1,9,07.90)(1,10,07.90)(1,11,07.90)(1,12,08.00)(1,13,08.00)(1,14,08.00)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.90)(5,2,00.90)(5,3,00.90)(5,4,01.20)(5,5,01.20)(5,6,01.20)(5,7,01.20)(5,8,01.80)(5,9,01.80)(5,10,01.80)(5,11,01.80)(5,12,02.40)(5,13,02.40)(5,14,02.40)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,07.60)(1,2,07.60)(1,3,07.60)(1,4,07.80)(1,5,07.80)(1,6,07.80)(1,7,07.80)(1,8,08.10)(1,9,08.10)(1,10,08.10)(1,11,08.10)(1,12,08.30)(1,13,08.30)(1,14,08.30)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,03.00)(5,2,03.00)(5,3,03.00)(5,4,02.70)(5,5,02.70)(5,6,02.70)(5,7,02.70)(5,8,03.70)(5,9,03.70)(5,10,03.70)(5,11,03.70)(5,12,04.30)(5,13,04.30)(5,14,04.30)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,01.40)(9,2,01.40)(9,3,01.40)(9,4,00.50)(9,5,00.50)(9,6,00.50)(9,7,00.50)(9,8,00.50)(9,9,00.50)(9,10,00.50)(9,11,00.50)(9,12,00.50)(9,13,00.50)(9,14,00.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,07.10)(1,2,05.9)(1,3,05.80)(1,4,05.80)(1,5,05.2)(1,6,06.70)(1,7,05.70)(1,8,07.50)(1,9,07.30)(1,10,07.20)(1,11,07.60)(1,12,08.40)(1,13,08.70)(1,14,08.10)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,01.00)(5,2,01.00)(5,3,01.10)(5,4,01.4)(5,5,01.50)(5,6,01.50)(5,7,01.30)(5,8,02.10)(5,9,01.90)(5,10,01.80)(5,11,02.0)(5,12,02.7)(5,13,02.6)(5,14,02.8)
%%\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.100)(9,3,0.000)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,06.80)(1,2,06.30)(1,3,06.70)(1,4,07.80)(1,5,06.80)(1,6,07.50)(1,7,07.80)(1,8,08.00)(1,9,08.60)(1,10,08.20)(1,11,08.20)(1,12,08.60)(1,13,08.50)(1,14,08.3)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,02.40)(5,2,02.6)(5,3,02.50)(5,4,02.40)(5,5,02.5)(5,6,02.60)(5,7,02.60)(5,8,03.60)(5,9,03.3)(5,10,02.80)(5,11,02.90)(5,12,04.2)(5,13,04.20)(5,14,04.20)
%%\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,01.10)(9,2,00.90)(9,3,01.00)(9,4,00.60)(9,5,00.50)(9,6,00.50)(9,7,00.5)(9,8,00.50)(9,9,00.60)(9,10,00.50)(9,11,00.60)(9,12,00.50)(9,13,00.60)(9,14,00.70)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,10.00)(1,2,10.00)(1,3,10.00)(1,4,10.0)(1,5,10.0)(1,6,10.0)(1,7,10.0)(1,8,10.00)(1,9,10.00)(1,10,10.00)(1,11,10.00)(1,12,10.00)(1,13,10.00)(1,14,10.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,08.50)(5,2,08.50)(5,3,08.50)(5,4,03.70)(5,5,03.70)(5,6,03.70)(5,7,03.70)(5,8,03.3)(5,9,03.3)(5,10,03.3)(5,11,03.3)(5,12,03.3)(5,13,03.3)(5,14,03.3)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,07.00)(9,2,07.00)(9,3,07.00)(9,4,00.4)(9,5,00.4)(9,6,00.4)(9,7,00.4)(9,8,00.4)(9,9,00.4)(9,10,00.4)(9,11,00.4)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,06.30)(1,2,06.30)(1,3,06.00)(1,4,06.3)(1,5,06.3)(1,6,07.30)(1,7,07.30)(1,8,07.70)(1,9,08.00)(1,10,08.60)(1,11,07.80)(1,12,07.50)(1,13,07.90)(1,14,08.20)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,04.10)(5,2,04.20)(5,3,04.30)(5,4,02.00)(5,5,01.60)(5,6,01.80)(5,7,01.80)(5,8,05.0)(5,9,05.0)(5,10,05.0)(5,11,05.0)(5,12,05.0)(5,13,05.0)(5,14,05.0)
%%\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,03.4)(9,2,03.30)(9,3,03.30)(9,4,00.10)(9,5,00.20)(9,6,00.2)(9,7,00.1)(9,8,00.20)(9,9,00.20)(9,10,00.2)(9,11,00.2)(9,12,00.30)(9,13,00.20)(9,14,00.10)
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}
%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%
\end{pspicture}
}
%
\end{minipage}
%%

\vspace*{0.1in}
\caption{\label{newfig4}Effect of variations of the total external to internal asset ratio $E/I$ on the vulnerability index $\xi$ for homogeneous networks.
Lower values of $\xi$ imply higher global stability of a network.}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


















%%%\thispagestyle{empty}

\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig5
%%\input{../tex-figures/newfig5-coordinated-only.tex}

\begin{figure*}
%
\vspace*{0.5in}
%
\hspace*{0.0in}
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(1,-3)(5,2)
\psset{xunit=0.010in,yunit=2.5in}
\rput(175,-0.15){\bf (A)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.8,Dx=25,Dy=0.1](328,0.25)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.25)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.25)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](300,0.61)(335,0.61)
\rput[mr](285,0.61){\bf\footnotesize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](665,0.61)(700,0.61)
\rput[mr](655,0.61){\bf\footnotesize {\sf ER} model (average degree $3$), coordinated shock}
%%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](300,1.48)(335,1.48)
%\rput[mr](285,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), random shock}
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](665,1.48)(700,1.48)
%\rput[mr](655,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](300,0.54)(335,0.54)
\rput[mr](285,0.54){\bf\footnotesize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](665,0.54)(700,0.54)
\rput[mr](655,0.54){\bf\footnotesize {\sf SF} model (average degree $3$), coordinated shock}
%%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](300,1.34)(335,1.34)
%\rput[mr](285,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), random shock}
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](665,1.34)(700,1.34)
%\rput[mr](655,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](500,0.47)(535,0.47)
\rput[mr](485,0.47){\bf\footnotesize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](735,1.27)(770,1.27)
%\rput[mr](725,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), random shock}
%
\rput[ml](0.10,0.37){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,0.3){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
%
\rput[mr](-35,0.125){$\pmb{\xi}$}
%
\psset{origin={-25,-0.8}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.88)(050,0.88)(075,0.88)(100,0.88)(125,0.88)(150,0.88)(175,0.88)(200,0.88)(225,0.88)(250,0.88)(275,0.88)(300,0.88)(325,0.88)(350,0.88)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.92)(050,0.96)(075,0.26)(100,0.36)(125,0.40)(150,0.96)(175,0.94)(200,0.46)(225,0.94)(250,0.96)(275,0.96)(300,0.34)(325,1.00)(350,0.36)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.76)(050,0.90)(075,0.82)(100,0.72)(125,0.84)(150,0.86)(175,0.82)(200,0.88)(225,0.48)(250,0.74)(275,0.74)(300,0.72)(325,0.48)(350,0.86)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.94)(050,0.94)(075,0.94)(100,0.94)(125,0.94)(150,0.94)(175,0.94)(200,0.94)(225,0.94)(250,0.94)(275,0.94)(300,0.94)(325,0.94)(350,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,1.00)(050,0.08)(075,0.14)(100,0.10)(125,0.08)(150,1.00)(175,0.14)(200,0.16)(225,1.00)(250,0.12)(275,1.00)(300,0.14)(325,1.00)(350,0.12)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.08)(050,0.10)(075,0.94)(100,0.94)(125,0.94)(150,0.10)(175,0.18)(200,0.94)(225,0.96)(250,0.08)(275,0.08)(300,0.10)(325,0.96)(350,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.14)(050,0.20)(075,0.10)(100,0.22)(125,0.28)(150,0.34)(175,0.26)(200,0.10)(225,0.30)(250,0.28)(275,0.22)(300,0.80)(325,0.40)(350,0.74)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
%%%%%%%%%%%%
\end{minipage}
%
\hspace*{0.1in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(-3,-3)(-1,2)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (B)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.8,Dx=25,Dy=0.1](328,0.25)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.25)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.25)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.125){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.37){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,0.3){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%
\psset{origin={-25,-0.8}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.96)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.82)(050,0.84)(075,0.86)(100,0.86)(125,0.86)(150,0.86)(175,0.86)(200,0.86)(225,0.86)(250,0.86)(275,0.86)(300,0.86)(325,0.86)(350,0.86)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.00)(050,0.06)(075,0.10)(100,0.68)(125,1.00)(150,0.64)(175,0.10)(200,0.08)(225,0.84)(250,0.10)(275,1.00)(300,0.08)(325,0.08)(350,0.76)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.08)(050,0.08)(075,0.10)(100,0.10)(125,0.84)(150,0.82)(175,0.82)(200,0.08)(225,0.10)(250,0.10)(275,0.14)(300,0.10)(325,0.12)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.84)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.82)(050,0.94)(075,0.94)(100,0.94)(125,0.94)(150,0.94)(175,0.94)(200,0.94)(225,0.94)(250,0.94)(275,0.94)(300,0.94)(325,0.94)(350,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,0.02)(100,0.04)(125,1.00)(150,1.00)(175,1.00)(200,0.06)(225,1.00)(250,0.10)(275,0.08)(300,1.00)(325,1.00)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.06)(050,0.08)(075,0.94)(100,0.94)(125,0.10)(150,0.08)(175,0.10)(200,0.08)(225,0.10)(250,0.10)(275,0.10)(300,0.94)(325,0.94)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.82)(050,0.82)(075,0.82)(100,0.82)(125,0.82)(150,0.82)(175,0.82)(200,0.82)(225,0.82)(250,0.82)(275,0.82)(300,0.82)(325,0.82)(350,0.82)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.90)(050,0.10)(075,0.10)(100,0.10)(125,0.74)(150,0.10)(175,0.78)(200,0.10)(225,0.10)(250,0.10)(275,0.76)(300,0.26)(325,0.10)(350,0.10)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
\end{minipage}
\\
\hspace*{-0.0in}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(1,-5.4)(3,5.6)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (C)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,0.95)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.95)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.95)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.45){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,1.07){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,1.0){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.45}$}
%
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.06)(050,0.22)(075,0.44)(100,0.52)(125,0.52)(150,0.56)(175,0.60)(200,0.64)(225,0.66)(250,0.72)(275,0.76)(300,0.80)(325,0.82)(350,0.76)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.28)(050,0.40)(075,0.50)(100,0.54)(125,0.56)(150,0.60)(175,0.62)(200,0.64)(225,0.66)(250,0.66)(275,0.66)(300,0.66)(325,0.68)(350,0.68)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.02)(050,0.00)(075,0.00)(100,0.04)(125,0.16)(150,0.00)(175,0.16)(200,0.20)(225,0.18)(250,0.08)(275,0.00)(300,0.18)(325,0.16)(350,0.20)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.02)(050,0.20)(075,0.08)(100,0.04)(125,0.06)(150,0.02)(175,0.22)(200,0.06)(225,0.04)(250,0.06)(275,0.90)(300,0.10)(325,0.10)(350,0.04)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.00)(050,0.00)(075,0.04)(100,0.06)(125,0.14)(150,0.24)(175,0.30)(200,0.30)(225,0.44)(250,0.48)(275,0.56)(300,0.62)(325,0.66)(350,0.60)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.00)(050,0.02)(075,0.06)(100,0.18)(125,0.24)(150,0.28)(175,0.32)(200,0.32)(225,0.36)(250,0.36)(275,0.46)(300,0.46)(325,0.46)(350,0.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.04)(050,0.02)(075,0.02)(100,0.04)(125,0.10)(150,0.10)(175,0.04)(200,0.04)(225,0.06)(250,0.06)(275,0.06)(300,0.04)(325,0.06)(350,0.06)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.04)(050,0.10)(075,0.08)(100,0.10)(125,0.04)(150,0.10)(175,0.10)(200,0.08)(225,0.08)(250,0.06)(275,0.06)(300,0.06)(325,0.08)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.22)(050,0.26)(075,0.26)(100,0.30)(125,0.30)(150,0.30)(175,0.30)(200,0.30)(225,0.30)(250,0.30)(275,0.30)(300,0.30)(325,0.30)(350,0.30)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.00)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
%
\end{minipage}
%
\hspace*{-0.2in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(-1.75,-9.9)(-3.75,1.1)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (D)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.8,Dx=25,Dy=0.1](328,0.25)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.25)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.25)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.25)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.1){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.37){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,0.3){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%
\psset{origin={-25,-0.8}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.99)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.94)(050,0.91)(075,0.91)(100,0.91)(125,0.92)(150,0.93)(175,0.93)(200,0.93)(225,0.94)(250,0.94)(275,0.94)(300,0.94)(325,0.94)(350,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.05)(050,0.58)(075,0.85)(100,0.70)(125,0.89)(150,0.96)(175,0.93)(200,0.92)(225,0.94)(250,0.90)(275,0.08)(300,0.93)(325,0.96)(350,0.85)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.07)(050,0.91)(075,0.78)(100,0.83)(125,0.09)(150,0.85)(175,0.90)(200,0.10)(225,0.10)(250,0.82)(275,0.10)(300,0.90)(325,0.85)(350,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.90)(050,0.99)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.88)(050,0.91)(075,0.91)(100,0.91)(125,0.91)(150,0.91)(175,0.91)(200,0.91)(225,0.91)(250,0.91)(275,0.91)(300,0.91)(325,0.91)(350,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.24)(050,0.08)(075,0.05)(100,0.09)(125,0.07)(150,0.09)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,0.10)(325,0.13)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.09)(050,0.91)(075,0.91)(100,0.09)(125,0.08)(150,0.92)(175,0.92)(200,0.92)(225,0.91)(250,0.90)(275,0.10)(300,0.10)(325,0.92)(350,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.99)(050,0.99)(075,0.99)(100,0.99)(125,0.99)(150,0.99)(175,0.99)(200,0.99)(225,0.99)(250,0.99)(275,0.99)(300,0.99)(325,0.99)(350,0.99)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.31)(050,0.10)(075,0.21)(100,0.20)(125,0.46)(150,0.21)(175,0.26)(200,0.40)(225,0.41)(250,0.10)(275,0.10)(300,0.25)(325,0.10)(350,0.35)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\scalebox{0.95}[0.7]{
\begin{pspicture}(0.5,-4.8)(-1.5,6.2)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (E)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.6,Dx=25,Dy=0.1](328,0.45)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.45)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.45)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.2){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](50,0.52){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](50,0.45){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
\psset{origin={-25,-0.6}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.97)(050,0.99)(075,0.99)(100,0.99)(125,0.99)(150,0.97)(175,0.97)(200,0.97)(225,0.98)(250,0.98)(275,0.98)(300,0.97)(325,0.98)(350,0.98)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.90)(050,0.89)(075,0.89)(100,0.88)(125,0.89)(150,0.89)(175,0.89)(200,0.86)(225,0.86)(250,0.86)(275,0.87)(300,0.87)(325,0.87)(350,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.91)(050,0.92)(075,0.93)(100,0.92)(125,0.93)(150,0.94)(175,0.96)(200,0.92)(225,0.93)(250,0.91)(275,0.98)(300,0.91)(325,0.90)(350,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.92)(050,0.73)(075,0.68)(100,0.80)(125,0.82)(150,0.80)(175,0.76)(200,0.82)(225,0.89)(250,0.86)(275,0.62)(300,0.68)(325,0.69)(350,0.57)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.98)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.95)(050,0.97)(075,0.97)(100,0.97)(125,0.97)(150,0.97)(175,0.97)(200,0.97)(225,0.97)(250,0.97)(275,0.97)(300,0.97)(325,0.97)(350,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.99)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,0.98)(225,0.98)(250,0.92)(275,1.00)(300,1.00)(325,0.98)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.92)(050,0.97)(075,0.91)(100,0.93)(125,0.89)(150,0.96)(175,0.94)(200,0.97)(225,0.95)(250,0.93)(275,0.92)(300,0.88)(325,0.96)(350,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.67)(050,0.67)(075,0.67)(100,0.67)(125,0.67)(150,0.67)(175,0.67)(200,0.67)(225,0.67)(250,0.67)(275,0.67)(300,0.67)(325,0.67)(350,0.67)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.71)(050,0.85)(075,0.84)(100,0.76)(125,0.69)(150,0.78)(175,0.83)(200,0.83)(225,0.66)(250,0.63)(275,0.79)(300,0.83)(325,0.70)(350,0.77)
%
\psset{origin={0,0}}
\end{pspicture}
}
\end{minipage}
%
\\
\hspace*{-0.0in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(1,-6.9)(3,-1.9)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (F)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.90,Dx=25,Dy=0.10](328,0.15)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.15)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.15)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.05){$\pmb{\xi}$}
%
\psset{origin={-25,-0.90}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.27){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,0.20){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.98)(050,0.99)(075,0.99)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.90)(050,0.94)(075,0.95)(100,0.96)(125,0.96)(150,0.96)(175,0.96)(200,0.96)(225,0.96)(250,0.96)(275,0.96)(300,0.96)(325,0.96)(350,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.90)(050,0.94)(075,0.96)(100,0.94)(125,0.97)(150,0.98)(175,0.94)(200,0.96)(225,0.95)(250,0.98)(275,0.95)(300,0.99)(325,0.93)(350,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.84)(050,0.87)(075,0.91)(100,0.93)(125,0.93)(150,0.93)(175,0.91)(200,0.85)(225,0.98)(250,0.93)(275,0.90)(300,0.93)(325,0.88)(350,0.89)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.97)(050,0.97)(075,0.97)(100,0.97)(125,0.97)(150,0.97)(175,0.97)(200,0.97)(225,0.97)(250,0.97)(275,0.97)(300,0.97)(325,0.97)(350,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,0.96)(100,1.00)(125,1.00)(150,0.99)(175,0.99)(200,0.98)(225,0.99)(250,0.99)(275,0.99)(300,0.99)(325,0.99)(350,0.99)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.91)(050,0.94)(075,0.96)(100,0.95)(125,0.95)(150,0.93)(175,0.92)(200,0.91)(225,0.95)(250,0.96)(275,0.92)(300,0.93)(325,0.95)(350,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.97)(050,0.97)(075,0.97)(100,0.97)(125,0.97)(150,0.97)(175,0.97)(200,0.97)(225,0.97)(250,0.97)(275,0.97)(300,0.97)(325,0.97)(350,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.83)(050,0.87)(075,0.87)(100,0.92)(125,0.85)(150,0.97)(175,0.79)(200,0.82)(225,0.78)(250,0.84)(275,0.95)(300,0.91)(325,0.94)(350,0.90)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 7 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(-3.75,-3)(-1.75,2)
\psset{xunit=0.010in,yunit=2.5in}
\rput(175,-0.15){\bf (G)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.4,Dx=25,Dy=0.1](328,0.65)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.65)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.65)
\comment{
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](300,1.15)(335,1.15)
\rput[mr](285,1.15){\bf\footnotesize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](665,1.15)(700,1.15)
\rput[mr](655,1.15){\bf\footnotesize {\sf ER} model (average degree $3$), coordinated shock}
%%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](300,1.48)(335,1.48)
%%\rput[mr](285,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), random shock}
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](665,1.48)(700,1.48)
%%\rput[mr](655,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](300,1.01)(335,1.01)
\rput[mr](285,1.01){\bf\footnotesize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](665,1.01)(700,1.01)
\rput[mr](655,1.01){\bf\footnotesize {\sf SF} model (average degree $3$), coordinated shock}
%%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](300,1.34)(335,1.34)
%%\rput[mr](285,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), random shock}
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](665,1.34)(700,1.34)
%%\rput[mr](655,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), random shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](350,0.87)(385,0.87)
\rput[mr](335,0.87){\bf\footnotesize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](735,1.27)(770,1.27)
%%\rput[mr](725,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), random shock}
%
}
\rput[ml](0.10,0.77){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.7){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.3){$\pmb{\xi}$}
%
\psset{origin={-25,-0.4}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.96)(050,0.98)(075,0.98)(100,0.98)(125,0.98)(150,0.98)(175,0.98)(200,0.98)(225,0.98)(250,0.98)(275,0.98)(300,0.98)(325,0.98)(350,0.98)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,1)(050,0.78)(075,0.80)(100,0.80)(125,0.80)(150,0.84)(175,0.84)(200,0.84)(225,0.84)(250,0.84)(275,0.84)(300,0.84)(325,0.84)(350,0.84)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,1.00)(050,0.58)(075,0.96)(100,0.42)(125,0.62)(150,0.48)(175,0.96)(200,0.84)(225,0.96)(250,0.94)(275,0.98)(300,0.94)(325,0.66)(350,0.88)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.54)(050,0.84)(075,0.86)(100,0.28)(125,0.90)(150,0.88)(175,0.64)(200,0.70)(225,0.64)(250,0.84)(275,0.38)(300,0.58)(325,0.90)(350,0.58)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.96)(050,0.96)(075,0.96)(100,0.96)(125,0.96)(150,0.96)(175,0.96)(200,0.96)(225,0.96)(250,0.96)(275,0.96)(300,0.96)(325,0.96)(350,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.78)(050,0.80)(075,0.80)(100,0.80)(125,0.80)(150,0.80)(175,0.80)(200,0.80)(225,0.80)(250,0.80)(275,0.80)(300,0.80)(325,0.80)(350,0.80)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.12)(050,0.40)(075,0.16)(100,0.46)(125,0.68)(150,0.62)(175,0.20)(200,0.16)(225,0.88)(250,0.72)(275,0.74)(300,0.84)(325,0.18)(350,0.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.86)(050,0.38)(075,0.16)(100,0.16)(125,0.54)(150,0.60)(175,0.38)(200,0.66)(225,0.40)(250,0.84)(275,0.78)(300,0.20)(325,0.24)(350,0.24)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.46)(050,0.44)(075,0.44)(100,0.44)(125,0.44)(150,0.44)(175,0.44)(200,0.44)(225,0.44)(250,0.44)(275,0.44)(300,0.44)(325,0.44)(350,0.44)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.18)(050,0.22)(075,0.42)(100,0.26)(125,0.24)(150,0.14)(175,0.16)(200,0.24)(225,0.12)(250,0.12)(275,0.10)(300,0.38)(325,0.32)(350,0.16)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
\end{minipage}
%
\\
\hspace*{-0.0in}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 8 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(1,-9)(3,-2)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (H)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,0.35)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.35)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.35)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.15){$\pmb{\xi}$}
%
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.47){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.4){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.18)(050,0.24)(075,0.24)(100,0.26)(125,0.26)(150,0.26)(175,0.26)(200,0.26)(225,0.26)(250,0.26)(275,0.26)(300,0.26)(325,0.26)(350,0.26)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.20)(050,0.24)(075,0.28)(100,0.28)(125,0.28)(150,0.28)(175,0.28)(200,0.28)(225,0.28)(250,0.28)(275,0.28)(300,0.28)(325,0.28)(350,0.28)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.08)(050,0.12)(075,0.10)(100,0.14)(125,0.10)(150,0.14)(175,0.10)(200,0.12)(225,0.10)(250,0.16)(275,0.12)(300,0.12)(325,0.10)(350,0.32)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.16)(050,0.96)(075,0.94)(100,0.12)(125,0.14)(150,0.12)(175,0.10)(200,0.10)(225,0.18)(250,0.10)(275,0.20)(300,0.92)(325,0.10)(350,0.20)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.12)(200,0.12)(225,0.12)(250,0.12)(275,0.12)(300,0.12)(325,0.12)(350,0.12)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.14)(050,0.16)(075,0.20)(100,0.20)(125,0.20)(150,0.20)(175,0.20)(200,0.20)(225,0.20)(250,0.20)(275,0.20)(300,0.20)(325,0.20)(350,0.20)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.10)(050,0.12)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.14)(275,0.10)(300,0.12)(325,0.12)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.12)(100,0.14)(125,0.10)(150,0.10)(175,0.10)(200,0.12)(225,0.12)(250,0.10)(275,0.10)(300,0.10)(325,0.12)(350,0.78)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.18)(050,0.18)(075,0.18)(100,0.18)(125,0.18)(150,0.18)(175,0.18)(200,0.18)(225,0.18)(250,0.18)(275,0.18)(300,0.18)(325,0.18)(350,0.18)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.14)(100,0.14)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.14)(275,0.10)(300,0.16)(325,0.10)(350,0.10)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
\end{minipage}
%
%
\\
\hspace*{-0.0in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 9 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(1,-12.7)(3,-5.7)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (I)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,0.15)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.15)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.15)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.05){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.27){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.2){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.45}$}
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.00)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.00)(050,0.06)(075,0.04)(100,0.06)(125,0.06)(150,0.06)(175,0.10)(200,0.06)(225,0.10)(250,0.08)(275,0.08)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.06)(050,0.08)(075,0.06)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.00)(050,0.00)(075,0.02)(100,0.08)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.00)(050,0.00)(075,0.02)(100,0.08)(125,0.08)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.00)(050,0.02)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.04)(050,0.06)(075,0.08)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.04)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 10 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(-3.75,-11.3)(-1.75,-6.3)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (J)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.1,Dx=25,Dy=0.1](328,0.35)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.35)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.35)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.15){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.47){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.4){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%
\psset{origin={-25,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.27)(050,0.30)(075,0.30)(100,0.34)(125,0.36)(150,0.36)(175,0.36)(200,0.36)(225,0.36)(250,0.36)(275,0.36)(300,0.36)(325,0.36)(350,0.36)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.37)(050,0.40)(075,0.40)(100,0.40)(125,0.40)(150,0.40)(175,0.40)(200,0.40)(225,0.40)(250,0.40)(275,0.40)(300,0.40)(325,0.40)(350,0.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.13)(050,0.10)(075,0.14)(100,0.15)(125,0.12)(150,0.11)(175,0.16)(200,0.12)(225,0.12)(250,0.15)(275,0.10)(300,0.10)(325,0.13)(350,0.11)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.19)(050,0.93)(075,0.15)(100,0.15)(125,0.87)(150,0.82)(175,0.13)(200,0.10)(225,0.17)(250,0.90)(275,0.12)(300,0.93)(325,0.10)(350,0.88)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.12)(050,0.15)(075,0.15)(100,0.16)(125,0.16)(150,0.16)(175,0.16)(200,0.17)(225,0.17)(250,0.17)(275,0.17)(300,0.17)(325,0.17)(350,0.17)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.12)(050,0.12)(075,0.12)(100,0.12)(125,0.13)(150,0.15)(175,0.15)(200,0.15)(225,0.15)(250,0.15)(275,0.15)(300,0.15)(325,0.15)(350,0.15)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.11)(225,0.10)(250,0.10)(275,0.11)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.11)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.11)(225,0.10)(250,0.11)(275,0.10)(300,0.11)(325,0.11)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.25)(050,0.25)(075,0.25)(100,0.25)(125,0.25)(150,0.25)(175,0.25)(200,0.25)(225,0.25)(250,0.25)(275,0.25)(300,0.25)(325,0.25)(350,0.25)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.17)(050,0.12)(075,0.10)(100,0.10)(125,0.18)(150,0.11)(175,0.15)(200,0.17)(225,0.11)(250,0.10)(275,0.12)(300,0.10)(325,0.17)(350,0.18)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
\end{minipage}
%
\\
\hspace*{-0.0in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 11 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(1,-15)(3,-8)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (K)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.5,Dx=25,Dy=0.1](328,0.45)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.45)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.45)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.2){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](50,0.52){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](50,0.45){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
\psset{origin={-25,-0.5}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.80)(050,0.84)(075,0.86)(100,0.86)(125,0.88)(150,0.88)(175,0.89)(200,0.89)(225,0.89)(250,0.89)(275,0.89)(300,0.89)(325,0.89)(350,0.89)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.81)(050,0.81)(075,0.81)(100,0.82)(125,0.82)(150,0.82)(175,0.82)(200,0.82)(225,0.82)(250,0.82)(275,0.82)(300,0.82)(325,0.82)(350,0.82)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,1.00)(050,0.66)(075,0.75)(100,0.92)(125,0.60)(150,0.75)(175,0.65)(200,0.93)(225,0.82)(250,0.88)(275,0.95)(300,0.78)(325,0.92)(350,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.70)(050,0.84)(075,0.74)(100,0.68)(125,0.59)(150,0.69)(175,0.81)(200,0.65)(225,0.78)(250,0.69)(275,0.70)(300,0.63)(325,0.76)(350,0.71)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.52)(050,0.55)(075,0.55)(100,0.56)(125,0.56)(150,0.56)(175,0.56)(200,0.57)(225,0.57)(250,0.57)(275,0.57)(300,0.57)(325,0.57)(350,0.57)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.52)(050,0.52)(075,0.52)(100,0.52)(125,0.53)(150,0.55)(175,0.55)(200,0.55)(225,0.55)(250,0.55)(275,0.55)(300,0.55)(325,0.55)(350,0.55)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.52)(050,0.55)(075,0.55)(100,0.58)(125,0.58)(150,0.54)(175,0.57)(200,0.54)(225,0.74)(250,0.55)(275,0.67)(300,0.51)(325,0.56)(350,0.69)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.50)(050,0.51)(075,0.56)(100,0.53)(125,0.55)(150,0.53)(175,0.53)(200,0.51)(225,0.52)(250,0.52)(275,0.51)(300,0.59)(325,0.54)(350,0.56)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.56)(050,0.56)(075,0.56)(100,0.56)(125,0.56)(150,0.56)(175,0.56)(200,0.56)(225,0.56)(250,0.56)(275,0.56)(300,0.56)(325,0.56)(350,0.56)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.55)(050,0.60)(075,0.54)(100,0.55)(125,0.60)(150,0.53)(175,0.53)(200,0.52)(225,0.56)(250,0.55)(275,0.53)(300,0.57)(325,0.61)(350,0.59)
%
\psset{origin={0,0}}
\end{pspicture}
}
\end{minipage}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 12 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[c]{2in}
\scalebox{0.95}[0.7]{
\begin{pspicture}(-3.75,-15)(-1.75,-10)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.15){\bf (L)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.90,Dx=25,Dy=0.10](328,0.15)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.15)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.15)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.05){$\pmb{\xi}$}
%
\psset{origin={-25,-0.90}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.27){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.20){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.97)(050,0.97)(075,0.97)(100,0.97)(125,0.97)(150,0.97)(175,0.97)(200,0.97)(225,0.97)(250,0.97)(275,0.97)(300,0.97)(325,0.97)(350,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.98)(050,0.96)(075,0.99)(100,1.00)(125,0.97)(150,0.99)(175,0.97)(200,0.95)(225,0.98)(250,0.99)(275,0.96)(300,0.98)(325,0.98)(350,0.98)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.96)(050,0.94)(075,0.92)(100,0.96)(125,0.95)(150,0.93)(175,0.95)(200,0.94)(225,0.97)(250,0.93)(275,0.94)(300,0.96)(325,0.96)(350,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.97)(050,0.97)(075,0.97)(100,0.97)(125,0.97)(150,0.97)(175,0.97)(200,0.97)(225,0.97)(250,0.97)(275,0.97)(300,0.97)(325,0.97)(350,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.93)(050,0.93)(075,0.93)(100,0.93)(125,0.93)(150,0.93)(175,0.93)(200,0.93)(225,0.93)(250,0.93)(275,0.93)(300,0.93)(325,0.93)(350,0.93)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.90)(050,0.95)(075,0.93)(100,0.97)(125,0.94)(150,0.97)(175,0.95)(200,0.95)(225,0.97)(250,0.94)(275,0.92)(300,0.95)(325,0.93)(350,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.88)(050,0.88)(075,0.83)(100,0.95)(125,0.92)(150,0.88)(175,0.90)(200,0.85)(225,0.90)(250,0.89)(275,0.92)(300,0.85)(325,0.89)(350,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.98)(050,0.95)(075,0.95)(100,0.95)(125,0.95)(150,0.95)(175,0.95)(200,0.95)(225,0.95)(250,0.95)(275,0.95)(300,0.95)(325,0.95)(350,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.90)(050,0.76)(075,0.77)(100,0.92)(125,0.79)(150,0.78)(175,0.75)(200,0.78)(225,0.87)(250,0.67)(275,0.83)(300,0.85)(325,0.84)(350,0.82)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
\end{minipage}
\vspace*{-3.9in}
\caption{\label{newfig5}Effect of variations of the total external to internal asset ratio $\nicefrac{E}{I}$ on the vulnerability index $\xi$
for $(\alpha,\beta)$-heterogeneous networks. Lower values of $\xi$ imply higher global stability of a network.}
%
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




























%%\thispagestyle{empty}

\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%newfig1-coordinated-and-random
%%%\input{../tex-figures/newfig1-coordinated-and-random.tex}
%
\begin{figure*}
%
\renewcommand{\thesubfigure}{\hspace*{0.6in}\protect\raisebox{0.2in}[0in][0.0in]{(\Alph{subfigure})}}
\vspace*{0.8in}
\hspace*{0.0in}
%
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1.3,-1.8)(3.3,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.50)(0.46,1.50)
\rput[mr](0.70,1.55){\bf\footnotesize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.50)(1.16,1.50)
\rput[mr](1.40,1.55){\bf\footnotesize {\sf ER} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.43)(0.46,1.43)
\rput[mr](0.7,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](1.11,1.43)(1.16,1.43)
\rput[mr](1.40,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.41,1.36)(0.46,1.36)
\rput[mr](0.7,1.41){\bf\footnotesize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](1.11,1.36)(1.16,1.36)
\rput[mr](1.40,1.41){\bf\footnotesize {\sf SF} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.41,1.29)(0.46,1.29)
\rput[mr](0.7,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.29)(1.16,1.29)
\rput[mr](1.40,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.22)(0.76,1.22)
\rput[mr](1,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.15)(0.76,1.15)
\rput[mr](1,1.20){\bf\footnotesize in-arborescence (average degree $\approx 1$), idiosyncratic shock}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.002)(0.15,0.006)(0.20,0.012)(0.25,0.02)(0.30,0.03)(0.35,0.034)(0.40,0.056)(0.45,0.136)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.008)(0.15,0.014)(0.20,0.024)(0.25,0.04)(0.30,0.048)(0.35,0.066)(0.40,0.112)(0.45,0.314)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.004)(0.15,0.004)(0.20,0.016)(0.25,0.014)(0.30,0.022)(0.35,0.034)(0.40,0.128)(0.45,0.118)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.012)(0.15,0.012)(0.20,0.024)(0.25,0.026)(0.30,0.046)(0.35,0.232)(0.40,0.158)(0.45,0.676)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.00)(0.15,0.002)(0.20,0.004)(0.25,0.004)(0.30,0.006)(0.35,0.014)(0.40,0.0118)(0.45,0.692)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.008)(0.15,0.01)(0.20,0.01)(0.25,0.026)(0.30,0.048)(0.35,0.294)(0.40,0.382)(0.45,0.854)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.004)(0.15,0.004)(0.20,0.016)(0.25,0.014)(0.30,0.022)(0.35,0.024)(0.40,0.128)(0.45,0.118)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.012)(0.15,0.012)(0.20,0.024)(0.25,0.026)(0.30,0.046)(0.35,0.232)(0.40,0.158)(0.45,0.676)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.058)(0.15,0.078)(0.20,0.10)(0.25,0.184)(0.30,0.356)(0.35,0.472)(0.40,0.582)(0.45,0.74)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.006)(0.15,0.018)(0.20,0.016)(0.25,0.026)(0.30,0.096)(0.35,0.164)(0.40,0.106)(0.45,0.120)
\end{pspicture}
 }
}
\hspace*{1in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.01)(0.15,0.03)(0.20,0.066)(0.25,0.10)(0.30,0.144)(0.35,0.202)(0.40,0.318)(0.45,0.666)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.014)(0.10,0.040)(0.15,0.072)(0.20,0.014)(0.25,0.174)(0.30,0.236)(0.35,0.354)(0.40,0.516)(0.45,0.746)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.004)(0.15,0.022)(0.20,0.054)(0.25,0.078)(0.30,0.204)(0.35,0.19)(0.40,0.426)(0.45,0.902)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.022)(0.10,0.044)(0.15,0.062)(0.20,0.112)(0.25,0.182)(0.30,0.29)(0.35,0.438)(0.40,0.674)(0.45,0.832)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.006)(0.15,0.012)(0.20,0.052)(0.25,0.086)(0.30,0.144)(0.35,0.178)(0.40,0.498)(0.45,0.782)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.042)(0.10,0.048)(0.15,0.092)(0.20,0.232)(0.25,0.22)(0.30,0.350)(0.35,0.518)(0.40,0.70)(0.45,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.014)(0.15,0.022)(0.20,0.078)(0.25,0.122)(0.30,0.158)(0.35,0.196)(0.40,0.334)(0.45,0.592)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.032)(0.10,0.04)(0.15,0.106)(0.20,0.232)(0.25,0.184)(0.30,0.332)(0.35,0.484)(0.40,0.546)(0.45,0.764)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.092)(0.15,0.15)(0.20,0.354)(0.25,0.452)(0.30,0.766)(0.35,1)(0.40,1)(0.45,1)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[origin={-0.05,0},linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.014)(0.10,0.048)(0.15,0.082)(0.20,0.144)(0.25,0.21)(0.30,0.42)(0.35,0.592)(0.40,0.554)(0.45,0.762)
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.006)(0.15,0.026)(0.20,0.038)(0.25,0.068)(0.30,0.082)(0.35,0.118)(0.40,0.168)(0.45,0.392)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.028)(0.15,0.05)(0.20,0.084)(0.25,0.116)(0.30,0.142)(0.35,0.176)(0.40,0.350)(0.45,0.582)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.004)(0.15,0.016)(0.20,0.034)(0.25,0.084)(0.30,0.090)(0.35,0.104)(0.40,0.404)(0.45,0.78)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.014)(0.10,0.03)(0.15,0.042)(0.20,0.086)(0.25,0.12)(0.30,0.228)(0.35,0.314)(0.40,0.742)(0.45,0.738)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.002)(0.15,0.006)(0.20,0.018)(0.25,0.038)(0.30,0.046)(0.35,0.17)(0.40,0.21)(0.45,0.714)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.008)(0.10,0.028)(0.15,0.04)(0.20,0.056)(0.25,0.08)(0.30,0.102)(0.35,0.142)(0.40,0.536)(0.45,0.746)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.014)(0.15,0.026)(0.20,0.044)(0.25,0.098)(0.30,0.108)(0.35,0.118)(0.40,0.178)(0.45,0.364)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.024)(0.10,0.046)(0.15,0.078)(0.20,0.096)(0.25,0.138)(0.30,0.142)(0.35,0.162)(0.40,0.362)(0.45,0.606)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.04)(0.10,0.158)(0.15,0.20)(0.20,0.20)(0.25,0.20)(0.30,0.246)(0.35,0.452)(0.40,0.804)(0.45,0.934)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.006)(0.10,0.048)(0.15,0.068)(0.20,0.20)(0.25,0.20)(0.30,0.232)(0.35,0.306)(0.40,0.316)(0.45,0.444)
%
\end{pspicture}
}
}
%%%
\\
\hspace*{-0.0in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\renewcommand{\thesubfigure}{\hspace*{0.6in}\protect\raisebox{0.2in}[0in][0.0in]{(\Alph{subfigure})}}
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1,-1.8)(3,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.002)(0.15,0.007)(0.20,0.016)(0.25,0.022)(0.30,0.028)(0.35,0.036)(0.40,0.051)(0.45,0.14)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.007)(0.10,0.011)(0.15,0.015)(0.20,0.028)(0.25,0.043)(0.30,0.046)(0.35,0.063)(0.40,0.108)(0.45,0.234)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.001)(0.15,0.003)(0.20,0.007)(0.25,0.015)(0.30,0.039)(0.35,0.039)(0.40,0.241)(0.45,0.148)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.008)(0.15,0.016)(0.20,0.032)(0.25,0.036)(0.30,0.046)(0.35,0.228)(0.40,0.58)(0.45,0.679)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.00)(0.15,0.001)(0.20,0.003)(0.25,0.005)(0.30,0.012)(0.35,0.015)(0.40,0.226)(0.45,0.705)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.004)(0.10,0.005)(0.15,0.008)(0.20,0.014)(0.25,0.036)(0.30,0.047)(0.35,0.288)(0.40,0.441)(0.45,0.696)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.004)(0.15,0.004)(0.20,0.02)(0.25,0.018)(0.30,0.037)(0.35,0.049)(0.40,0.145)(0.45,0.34)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.008)(0.10,0.005)(0.15,0.006)(0.20,0.037)(0.25,0.054)(0.30,0.059)(0.35,0.054)(0.40,0.13)(0.45,0.344)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.054)(0.15,0.081)(0.20,0.112)(0.25,0.135)(0.30,0.405)(0.35,0.51)(0.40,0.608)(0.45,0.763)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.003)(0.10,0.01)(0.15,0.011)(0.20,0.014)(0.25,0.039)(0.30,0.094)(0.35,0.103)(0.40,0.135)(0.45,0.262)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
\hspace*{1in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.011)(0.15,0.029)(0.20,0.057)(0.25,0.107)(0.30,0.151)(0.35,0.205)(0.40,0.32)(0.45,0.673)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.027)(0.10,0.051)(0.15,0.082)(0.20,0.143)(0.25,0.215)(0.30,0.264)(0.35,0.381)(0.40,0.547)(0.45,0.76)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.008)(0.15,0.025)(0.20,0.046)(0.25,0.101)(0.30,0.157)(0.35,0.357)(0.40,0.629)(0.45,0.687)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.034)(0.10,0.058)(0.15,0.09)(0.20,0.217)(0.25,0.204)(0.30,0.40)(0.35,0.60)(0.40,0.735)(0.45,0.844)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.015)(0.15,0.023)(0.20,0.084)(0.25,0.122)(0.30,0.181)(0.35,0.203)(0.40,0.421)(0.45,0.712)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.052)(0.10,0.053)(0.15,0.081)(0.20,0.209)(0.25,0.272)(0.30,0.288)(0.35,0.453)(0.40,0.529)(0.45,0.784)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.008)(0.15,0.025)(0.20,0.046)(0.25,0.101)(0.30,0.157)(0.35,0.357)(0.40,0.629)(0.45,0.687)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.034)(0.10,0.058)(0.15,0.09)(0.20,0.217)(0.25,0.204)(0.30,0.40)(0.35,0.60)(0.40,0.735)(0.45,0.844)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.035)(0.10,0.076)(0.15,0.152)(0.20,0.296)(0.25,0.366)(0.30,0.769)(0.35,1)(0.40,1)(0.45,1)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.016)(0.10,0.035)(0.15,0.059)(0.20,0.142)(0.25,0.20)(0.30,0.38)(0.35,0.562)(0.40,0.576)(0.45,0.63)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.003)(0.10,0.007)(0.15,0.024)(0.20,0.044)(0.25,0.069)(0.30,0.09)(0.35,0.12)(0.40,0.178)(0.45,0.473)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.012)(0.10,0.035)(0.15,0.057)(0.20,0.087)(0.25,0.115)(0.30,0.144)(0.35,0.193)(0.40,0.304)(0.45,0.592)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.006)(0.15,0.02)(0.20,0.039)(0.25,0.072)(0.30,0.081)(0.35,0.108)(0.40,0.255)(0.45,0.819)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.01)(0.10,0.042)(0.15,0.059)(0.20,0.16)(0.25,0.116)(0.30,0.228)(0.35,0.46)(0.40,0.736)(0.45,0.705)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.003)(0.15,0.022)(0.20,0.031)(0.25,0.068)(0.30,0.085)(0.35,0.105)(0.40,0.297)(0.45,0.641)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.016)(0.10,0.129)(0.15,0.069)(0.20,0.244)(0.25,0.125)(0.30,0.137)(0.35,0.169)(0.40,0.371)(0.45,0.595)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.011)(0.15,0.031)(0.20,0.049)(0.25,0.10)(0.30,0.129)(0.35,0.145)(0.40,0.257)(0.45,0.258)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.011)(0.10,0.079)(0.15,0.08)(0.20,0.186)(0.25,0.156)(0.30,0.176)(0.35,0.255)(0.40,0.335)(0.45,0.533)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.042)(0.10,0.14)(0.15,0.20)(0.20,0.20)(0.25,0.20)(0.30,0.244)(0.35,0.445)(0.40,0.84)(0.45,0.953)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.005)(0.10,0.033)(0.15,0.095)(0.20,0.20)(0.25,0.20)(0.30,0.219)(0.35,0.278)(0.40,0.401)(0.45,0.367)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 7 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\hspace*{-0.0in}
%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{0.6in}(\Alph{subfigure})}
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1,-1.8)(3,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psset{origin={-0.05,0}}
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.00)(0.15,0.006)(0.20,0.011)(0.25,0.02)(0.30,0.028)(0.35,0.035)(0.40,0.147)(0.45,0.211)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.005)(0.10,0.013)(0.15,0.017)(0.20,0.026)(0.25,0.039)(0.30,0.049)(0.35,0.071)(0.40,0.113)(0.45,0.239)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.002)(0.15,0.006)(0.20,0.01)(0.25,0.02)(0.30,0.029)(0.35,0.125)(0.40,0.428)(0.45,0.81)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.012)(0.15,0.018)(0.20,0.027)(0.25,0.034)(0.30,0.125)(0.35,0.39)(0.40,0.836)(0.45,0.811)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.003)(0.15,0.004)(0.20,0.012)(0.25,0.019)(0.30,0.026)(0.35,0.115)(0.40,0.331)(0.45,0.772)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.008)(0.10,0.01)(0.15,0.013)(0.20,0.037)(0.25,0.049)(0.30,0.057)(0.35,0.161)(0.40,0.588)(0.45,0.711)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.012)(0.15,0.04)(0.20,0.062)(0.25,0.11)(0.30,0.133)(0.35,0.148)(0.40,0.174)(0.45,0.294)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.011)(0.10,0.011)(0.15,0.011)(0.20,0.038)(0.25,0.057)(0.30,0.054)(0.35,0.055)(0.40,0.206)(0.45,0.538)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.019)(0.10,0.051)(0.15,0.075)(0.20,0.101)(0.25,0.145)(0.30,0.415)(0.35,0.531)(0.40,0.645)(0.45,0.82)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.003)(0.10,0.006)(0.15,0.008)(0.20,0.017)(0.25,0.03)(0.30,0.071)(0.35,0.104)(0.40,0.172)(0.45,0.176)
%
\psset{origin={0,0}}
%
\end{pspicture}
 }
}
\hspace*{1in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 8 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%%%%%%%%%%
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.009)(0.15,0.027)(0.20,0.058)(0.25,0.111)(0.30,0.152)(0.35,0.202)(0.40,0.384)(0.45,0.665)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.023)(0.10,0.053)(0.15,0.084)(0.20,0.14)(0.25,0.206)(0.30,0.272)(0.35,0.38)(0.40,0.54)(0.45,0.781)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.009)(0.15,0.028)(0.20,0.059)(0.25,0.115)(0.30,0.139)(0.35,0.356)(0.40,0.819)(0.45,0.874)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.027)(0.10,0.051)(0.15,0.08)(0.20,0.208)(0.25,0.263)(0.30,0.613)(0.35,0.772)(0.40,0.799)(0.45,0.807)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.024)(0.15,0.031)(0.20,0.104)(0.25,0.152)(0.30,0.196)(0.35,0.283)(0.40,0.514)(0.45,0.788)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.075)(0.10,0.077)(0.15,0.081)(0.20,0.248)(0.25,0.307)(0.30,0.32)(0.35,0.404)(0.40,0.612)(0.45,0.822)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.002)(0.10,0.026)(0.15,0.029)(0.20,0.102)(0.25,0.151)(0.30,0.199)(0.35,0.221)(0.40,0.376)(0.45,0.654)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.067)(0.10,0.063)(0.15,0.064)(0.20,0.289)(0.25,0.271)(0.30,0.273)(0.35,0.385)(0.40,0.488)(0.45,0.763)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.02)(0.10,0.07)(0.15,0.14)(0.20,0.284)(0.25,0.368)(0.30,0.75)(0.35,0.981)(0.40,0.992)(0.45,1)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.01)(0.10,0.034)(0.15,0.063)(0.20,0.145)(0.25,0.189)(0.30,0.341)(0.35,0.513)(0.40,0.618)(0.45,0.658)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 9 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thesubfigure}{\vspace*{-0.3in}\hspace*{1in}(\Alph{subfigure})}
%%%
\subfigure[]{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.007)(0.15,0.016)(0.20,0.039)(0.25,0.073)(0.30,0.098)(0.35,0.124)(0.40,0.251)(0.45,0.484)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.012)(0.10,0.037)(0.15,0.06)(0.20,0.088)(0.25,0.124)(0.30,0.147)(0.35,0.192)(0.40,0.31)(0.45,0.573)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.007)(0.15,0.018)(0.20,0.04)(0.25,0.067)(0.30,0.092)(0.35,0.125)(0.40,0.571)(0.45,0.898)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.01)(0.10,0.034)(0.15,0.054)(0.20,0.083)(0.25,0.202)(0.30,0.361)(0.35,0.739)(0.40,0.874)(0.45,0.797)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.00)(0.10,0.01)(0.15,0.029)(0.20,0.053)(0.25,0.101)(0.30,0.12)(0.35,0.137)(0.40,0.218)(0.45,0.748)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.028)(0.10,0.085)(0.15,0.108)(0.20,0.114)(0.25,0.172)(0.30,0.176)(0.35,0.208)(0.40,0.354)(0.45,0.539)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.001)(0.10,0.012)(0.15,0.04)(0.20,0.062)(0.25,0.11)(0.30,0.133)(0.35,0.148)(0.40,0.174)(0.45,0.294)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.027)(0.10,0.088)(0.15,0.115)(0.20,0.194)(0.25,0.172)(0.30,0.175)(0.35,0.25)(0.40,0.302)(0.45,0.563)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.03)(0.10,0.12)(0.15,0.185)(0.20,0.20)(0.25,0.20)(0.30,0.25)(0.35,0.433)(0.40,0.803)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.005)(0.10,0.037)(0.15,0.087)(0.20,0.192)(0.25,0.197)(0.30,0.215)(0.35,0.274)(0.40,0.377)(0.45,0.382)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%
\vspace*{-0.3in}
\caption{\label{newfig1-full}Effect of variations of equity to asset ratio (with respect to shock) on the vulnerability index $\xi$ for homogeneous networks.
Lower values of $\xi$ imply higher global stability of a network.
}
%
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





















\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%newfig2-coordinated-and-random
%%%\input{../tex-figures/newfig2-coordinated-and-random.tex}

\begin{figure*}
%
\vspace*{0.4in}
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1.5,-1.8)(3.5,9)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(A)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.50)(0.46,1.50)
\rput[mr](0.70,1.55){\bf\footnotesize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.50)(1.16,1.50)
\rput[mr](1.40,1.55){\bf\footnotesize {\sf ER} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.43)(0.46,1.43)
\rput[mr](0.7,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](1.11,1.43)(1.16,1.43)
\rput[mr](1.40,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.41,1.36)(0.46,1.36)
\rput[mr](0.7,1.41){\bf\footnotesize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](1.11,1.36)(1.16,1.36)
\rput[mr](1.40,1.41){\bf\footnotesize {\sf SF} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.41,1.29)(0.46,1.29)
\rput[mr](0.7,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.29)(1.16,1.29)
\rput[mr](1.40,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.22)(0.76,1.22)
\rput[mr](1,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.71,1.15)(0.76,1.15)
\rput[mr](1,1.20){\bf\footnotesize in-arborescence (average degree $\approx 1$), idiosyncratic shock}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,0}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.476)(0.10,0.85)(0.15,0.95)(0.20,0.974)(0.25,0.986)(0.30,0.994)(0.35,0.996)(0.40,0.998)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.548)(0.10,0.798)(0.15,0.864)(0.20,0.89)(0.25,0.91)(0.30,0.918)(0.35,0.928)(0.40,0.936)(0.45,0.944)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.122)(0.10,0.176)(0.15,0.178)(0.20,0.242)(0.25,0.346)(0.30,0.358)(0.35,0.238)(0.40,0.332)(0.45,0.67)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.136)(0.10,0.26)(0.15,0.252)(0.20,0.234)(0.25,0.204)(0.30,0.20)(0.35,0.326)(0.40,0.496)(0.45,0.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.078)(0.10,0.684)(0.15,0.952)(0.20,0.984)(0.25,0.994)(0.30,1.00)(0.35,1.00)(0.40,1.00)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.12)(0.10,0.616)(0.15,0.752)(0.20,0.802)(0.25,0.836)(0.30,0.808)(0.35,0.814)(0.40,0.82)(0.45,0.898)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.054)(0.10,0.11)(0.15,0.136)(0.20,0.304)(0.25,0.274)(0.30,0.382)(0.35,0.33)(0.40,0.326)(0.45,0.454)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.084)(0.10,0.08)(0.15,0.178)(0.20,0.186)(0.25,0.168)(0.30,0.208)(0.35,0.102)(0.40,0.192)(0.45,0.39)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.516)(0.10,0.738)(0.15,0.828)(0.20,0.848)(0.25,0.87)(0.30,0.88)(0.35,0.896)(0.40,0.904)(0.45,0.942)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.148)(0.10,0.142)(0.15,0.176)(0.20,0.168)(0.25,0.216)(0.30,0.25)(0.35,0.164)(0.40,0.30)(0.45,0.234)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{1in}
%%%%%%%%%%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-1.8)(0.8,8)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.0,Dx=0.05,Dy=0.1](0.42,1.05)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(B)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
%
\psset{origin={-0.05,0.0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.56)(0.10,0.892)(0.15,0.974)(0.20,0.992)(0.25,1.00)(0.30,1.00)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.548)(0.10,0.798)(0.15,0.864)(0.20,0.89)(0.25,0.91)(0.30,0.918)(0.35,0.928)(0.40,0.936)(0.45,0.944)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.442)(0.10,0.644)(0.15,0.696)(0.20,0.776)(0.25,0.836)(0.30,0.886)(0.35,0.878)(0.40,0.888)(0.45,0.93)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.478)(0.10,0.596)(0.15,0.676)(0.20,0.70)(0.25,0.696)(0.30,0.75)(0.35,0.766)(0.40,0.816)(0.45,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.078)(0.10,0.916)(0.15,0.988)(0.20,0.99)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.36)(0.10,0.814)(0.15,0.882)(0.20,0.888)(0.25,0.94)(0.30,0.926)(0.35,0.94)(0.40,0.942)(0.45,0.946)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.232)(0.10,0.478)(0.15,0.734)(0.20,0.752)(0.25,0.826)(0.30,0.936)(0.35,0.912)(0.40,0.966)(0.45,0.896)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.408)(0.10,0.602)(0.15,0.646)(0.20,0.712)(0.25,0.768)(0.30,0.718)(0.35,0.684)(0.40,0.806)(0.45,0.854)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.606)(0.10,0.646)(0.15,0.646)(0.20,0.646)(0.25,0.646)(0.30,0.758)(0.35,0.862)(0.40,0.94)(0.45,0.992)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.568)(0.10,0.648)(0.15,0.646)(0.20,0.664)(0.25,0.652)(0.30,0.716)(0.35,0.702)(0.40,0.792)(0.45,0.82)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-2.8)(0.8,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(C)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.764)(0.10,0.978)(0.15,0.988)(0.20,0.996)(0.25,0.996)(0.30,0.998)(0.35,0.998)(0.40,0.996)(0.45,0.994)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.716)(0.10,0.856)(0.15,0.894)(0.20,0.91)(0.25,0.922)(0.30,0.924)(0.35,0.92)(0.40,0.912)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.238)(0.10,0.444)(0.15,0.544)(0.20,0.68)(0.25,0.702)(0.30,0.742)(0.35,0.638)(0.40,0.83)(0.45,0.892)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.242)(0.10,0.262)(0.15,0.452)(0.20,0.51)(0.25,0.40)(0.30,0.446)(0.35,0.742)(0.40,0.544)(0.45,0.728)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.624)(0.10,0.97)(0.15,0.996)(0.20,1.00)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.534)(0.10,0.858)(0.15,0.818)(0.20,0.82)(0.25,0.816)(0.30,0.866)(0.35,0.898)(0.40,0.84)(0.45,0.894)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.152)(0.10,0.334)(0.15,0.376)(0.20,0.424)(0.25,0.422)(0.30,0.442)(0.35,0.444)(0.40,0.582)(0.45,0.616)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.18)(0.10,0.378)(0.15,0.318)(0.20,0.392)(0.25,0.378)(0.30,0.35)(0.35,0.394)(0.40,0.64)(0.45,0.542)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.55)(0.10,0.622)(0.15,0.638)(0.20,0.64)(0.25,0.644)(0.30,0.69)(0.35,0.75)(0.40,0.818)(0.45,0.934)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.284)(0.10,0.288)(0.15,0.304)(0.20,0.244)(0.25,0.338)(0.30,0.234)(0.35,0.324)(0.40,0.436)(0.45,0.438)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1.5,-4.8)(3.5,7)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(D)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.116)(0.20,0.182)(0.25,0.298)(0.30,0.47)(0.35,0.60)(0.40,0.846)(0.45,0.98)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.118)(0.15,0.16)(0.20,0.25)(0.25,0.35)(0.30,0.462)(0.35,0.616)(0.40,0.758)(0.45,0.896)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.062)(0.10,0.084)(0.15,0.10)(0.20,0.106)(0.25,0.124)(0.30,0.132)(0.35,0.23)(0.40,0.264)(0.45,0.606)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.082)(0.10,0.096)(0.15,0.118)(0.20,0.226)(0.25,0.134)(0.30,0.244)(0.35,0.162)(0.40,0.42)(0.45,0.514)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.076)(0.10,0.10)(0.15,0.10)(0.20,0.10)(0.25,0.106)(0.30,0.258)(0.35,0.61)(0.40,0.884)(0.45,0.978)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.062)(0.10,0.10)(0.15,0.10)(0.20,0.102)(0.25,0.148)(0.30,0.278)(0.35,0.446)(0.40,0.722)(0.45,0.814)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.10,0.098)(0.10,0.10)(0.15,0.10)(0.20,0.102)(0.25,0.104)(0.30,0.102)(0.35,0.136)(0.40,0.232)(0.45,0.43)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.09)(0.10,0.10)(0.15,0.104)(0.20,0.11)(0.25,0.104)(0.30,0.132)(0.35,0.156)(0.40,0.19)(0.45,0.332)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.108)(0.15,0.126)(0.20,0.182)(0.25,0.262)(0.30,0.346)(0.35,0.544)(0.40,0.62)(0.45,0.784)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.106)(0.15,0.12)(0.20,0.112)(0.25,0.126)(0.30,0.17)(0.35,0.17)(0.40,0.202)(0.45,0.16)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(1.5,-4.8)(3.5,5)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(E)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
%
\psset{origin={-0.05,-0.3}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.316)(0.10,0.498)(0.15,0.568)(0.20,0.724)(0.25,0.892)(0.30,0.954)(0.35,0.978)(0.40,0.994)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.454)(0.10,0.542)(0.15,0.646)(0.20,0.748)(0.25,0.836)(0.30,0.866)(0.35,0.918)(0.40,0.958)(0.45,0.976)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.334)(0.10,0.476)(0.15,0.504)(0.20,0.546)(0.25,0.644)(0.30,0.748)(0.35,0.836)(0.40,0.922)(0.45,0.982)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.452)(0.10,0.516)(0.15,0.548)(0.20,0.582)(0.25,0.666)(0.30,0.736)(0.35,0.812)(0.40,0.892)(0.45,0.928)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.51)(0.20,0.544)(0.25,0.606)(0.30,0.736)(0.35,0.902)(0.40,0.978)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.516)(0.20,0.55)(0.25,0.622)(0.30,0.726)(0.35,0.808)(0.40,0.944)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.498)(0.10,0.50)(0.15,0.502)(0.20,0.51)(0.25,0.54)(0.30,0.672)(0.35,0.806)(0.40,0.92)(0.45,0.976)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.496)(0.10,0.50)(0.15,0.51)(0.20,0.518)(0.25,0.54)(0.30,0.618)(0.35,0.696)(0.40,0.862)(0.45,0.892)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.336)(0.10,0.36)(0.15,0.388)(0.20,0.446)(0.25,0.536)(0.30,0.678)(0.35,0.856)(0.40,0.938)(0.45,0.972)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.51)(0.15,0.528)(0.20,0.542)(0.25,0.552)(0.30,0.658)(0.35,0.716)(0.40,0.724)(0.45,0.822)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.8}[0.7]{
\begin{pspicture}(-0.8,-4.8)(0.8,5)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(F)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
%
\psset{origin={-0.05,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.212)(0.15,0.322)(0.20,0.522)(0.25,0.784)(0.30,0.902)(0.35,0.97)(0.40,0.984)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.258)(0.15,0.384)(0.20,0.548)(0.25,0.702)(0.30,0.796)(0.35,0.872)(0.40,0.928)(0.45,0.966)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.198)(0.10,0.20)(0.15,0.206)(0.20,0.224)(0.25,0.30)(0.30,0.344)(0.35,0.40)(0.40,0.702)(0.45,0.838)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.204)(0.15,0.232)(0.20,0.226)(0.25,0.272)(0.30,0.416)(0.35,0.442)(0.40,0.626)(0.45,0.754)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.212)(0.20,0.272)(0.25,0.376)(0.30,0.602)(0.35,0.84)(0.40,0.962)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.218)(0.20,0.268)(0.25,0.378)(0.30,0.54)(0.35,0.65)(0.40,0.884)(0.45,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.204)(0.25,0.218)(0.30,0.24)(0.35,0.286)(0.40,0.518)(0.45,0.882)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.218)(0.25,0.218)(0.30,0.246)(0.35,0.312)(0.40,0.486)(0.45,0.646)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.228)(0.15,0.27)(0.20,0.34)(0.25,0.454)(0.30,0.564)(0.35,0.762)(0.40,0.848)(0.45,0.942)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.206)(0.15,0.204)(0.20,0.204)(0.25,0.248)(0.30,0.244)(0.35,0.338)(0.40,0.35)(0.45,0.364)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%
\vspace*{-0.5in}
\caption{\label{newfig2-full}Effect of variations of equity to asset ratio (with respect to shock) on the vulnerability index $\xi$ for 
$(\alpha,\beta)$-heterogeneous networks. Lower values of $\xi$ imply higher global stability of a network.
}
%
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%












%%\thispagestyle{empty}

\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig3-coordinated-and-random
%%\input{../tex-figures/newfig3-coordinated-and-random.tex}

\begin{figure*}
%
\vspace*{1.2in}
%
%%\hspace*{0.0in}
%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-6.2)(3.5,4.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(A)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\psset{origin={0.3,0.05}}
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.50)(0.46,1.50)
\rput[mr](0.70,1.55){\bf\footnotesize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.50)(1.16,1.50)
\rput[mr](1.40,1.55){\bf\footnotesize {\sf ER} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.41,1.43)(0.46,1.43)
\rput[mr](0.7,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](1.11,1.43)(1.16,1.43)
\rput[mr](1.40,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.41,1.36)(0.46,1.36)
\rput[mr](0.7,1.41){\bf\footnotesize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](1.11,1.36)(1.16,1.36)
\rput[mr](1.40,1.41){\bf\footnotesize {\sf SF} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.41,1.29)(0.46,1.29)
\rput[mr](0.7,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](1.11,1.29)(1.16,1.29)
\rput[mr](1.40,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.41,1.22)(0.46,1.22)
\rput[mr](0.70,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1.11,1.22)(1.16,1.22)
\rput[mr](1.40,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), idiosyncratic shock}
%
\psset{origin={0,0}}
%
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.649)(0.10,0.938)(0.15,0.984)(0.20,0.992)(0.25,0.995)(0.30,0.999)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.65)(0.10,0.86)(0.15,0.914)(0.20,0.928)(0.25,0.932)(0.30,0.941)(0.35,0.945)(0.40,0.946)(0.45,0.949)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.113)(0.10,0.235)(0.15,0.338)(0.20,0.35)(0.25,0.513)(0.30,0.668)(0.35,0.738)(0.40,0.684)(0.45,0.806)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.14)(0.10,0.161)(0.15,0.262)(0.20,0.282)(0.25,0.309)(0.30,0.389)(0.35,0.526)(0.40,0.466)(0.45,0.721)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.229)(0.10,0.708)(0.15,0.915)(0.20,0.968)(0.25,0.991)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.241)(0.10,0.629)(0.15,0.853)(0.20,0.888)(0.25,0.90)(0.30,0.90)(0.35,0.90)(0.40,0.90)(0.45,0.90)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.049)(0.10,0.086)(0.15,0.144)(0.20,0.186)(0.25,0.338)(0.30,0.363)(0.35,0.421)(0.40,0.324)(0.45,0.605)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.093)(0.10,0.101)(0.15,0.219)(0.20,0.18)(0.25,0.203)(0.30,0.225)(0.35,0.241)(0.40,0.29)(0.45,0.554)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.449)(0.10,0.676)(0.15,0.74)(0.20,0.787)(0.25,0.815)(0.30,0.839)(0.35,0.86)(0.40,0.888)(0.45,0.928)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.138)(0.10,0.171)(0.15,0.149)(0.20,0.163)(0.25,0.162)(0.30,0.25)(0.35,0.206)(0.40,0.196)(0.45,0.366)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{1in}
%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-7.4)(0.8,3.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.5){$\pmb{\xi}$}
\rput(0.2,-0.2){(B)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
%
\psset{origin={-0.05,-0.3}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.701)(0.10,0.954)(0.15,0.991)(0.20,0.996)(0.25,0.996)(0.30,0.995)(0.35,0.993)(0.40,0.994)(0.45,0.995)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.77)(0.10,0.866)(0.15,0.892)(0.20,0.895)(0.25,0.894)(0.30,0.90)(0.35,0.905)(0.40,0.928)(0.45,0.955)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.525)(0.10,0.697)(0.15,0.755)(0.20,0.799)(0.25,0.884)(0.30,0.91)(0.35,0.925)(0.40,0.934)(0.45,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.545)(0.10,0.678)(0.15,0.658)(0.20,0.733)(0.25,0.772)(0.30,0.789)(0.35,0.818)(0.40,0.861)(0.45,0.911)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.284)(0.10,0.901)(0.15,0.968)(0.20,0.988)(0.25,0.995)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.488)(0.10,0.828)(0.15,0.947)(0.20,0.947)(0.25,0.947)(0.30,0.947)(0.35,0.948)(0.40,0.948)(0.45,0.948)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.31)(0.10,0.581)(0.15,0.73)(0.20,0.819)(0.25,0.83)(0.30,0.928)(0.35,0.975)(0.40,0.966)(0.45,0.984)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.442)(0.10,0.61)(0.15,0.681)(0.20,0.781)(0.25,0.788)(0.30,0.784)(0.35,0.804)(0.40,0.894)(0.45,0.934)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.529)(0.10,0.608)(0.15,0.608)(0.20,0.608)(0.25,0.609)(0.30,0.73)(0.35,0.809)(0.40,0.904)(0.45,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.598)(0.10,0.665)(0.15,0.638)(0.20,0.671)(0.25,0.621)(0.30,0.701)(0.35,0.767)(0.40,0.738)(0.45,0.827)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{1.8in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-7.2)(0.8,3.6)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(C)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.832)(0.10,0.984)(0.15,0.994)(0.20,0.998)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.768)(0.10,0.895)(0.15,0.915)(0.20,0.93)(0.25,0.931)(0.30,0.934)(0.35,0.936)(0.40,0.933)(0.45,0.933)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.241)(0.10,0.442)(0.15,0.614)(0.20,0.522)(0.25,0.768)(0.30,0.69)(0.35,0.871)(0.40,0.80)(0.45,0.909)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.28)(0.10,0.317)(0.15,0.435)(0.20,0.655)(0.25,0.549)(0.30,0.616)(0.35,0.629)(0.40,0.688)(0.45,0.822)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.521)(0.10,0.925)(0.15,0.968)(0.20,0.997)(0.25,0.998)(0.30,0.998)(0.35,0.998)(0.40,0.998)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.473)(0.10,0.825)(0.15,0.914)(0.20,0.916)(0.25,0.916)(0.30,0.916)(0.35,0.917)(0.40,0.917)(0.45,0.917)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.17)(0.10,0.236)(0.15,0.476)(0.20,0.57)(0.25,0.593)(0.30,0.626)(0.35,0.642)(0.40,0.74)(0.45,0.887)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.201)(0.10,0.415)(0.15,0.399)(0.20,0.448)(0.25,0.315)(0.30,0.437)(0.35,0.529)(0.40,0.598)(0.45,0.693)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.489)(0.10,0.626)(0.15,0.641)(0.20,0.646)(0.25,0.651)(0.30,0.70)(0.35,0.755)(0.40,0.84)(0.45,0.922)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.267)(0.10,0.27)(0.15,0.375)(0.20,0.241)(0.25,0.401)(0.30,0.372)(0.35,0.374)(0.40,0.476)(0.45,0.447)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-7.2)(3.5,2.6)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(D)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.79)(0.10,0.97)(0.15,0.99)(0.20,0.995)(0.25,0.996)(0.30,0.996)(0.35,0.997)(0.40,0.997)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.63)(0.10,0.77)(0.15,0.81)(0.20,0.84)(0.25,0.93)(0.30,0.94)(0.35,0.94)(0.40,0.94)(0.45,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.18)(0.10,0.25)(0.15,0.36)(0.20,0.47)(0.25,0.52)(0.30,0.63)(0.35,0.84)(0.40,0.84)(0.45,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.16)(0.10,0.24)(0.15,0.32)(0.20,0.36)(0.25,0.40)(0.30,0.52)(0.35,0.64)(0.40,0.64)(0.45,0.63)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.15)(0.10,0.38)(0.15,0.72)(0.20,0.90)(0.25,0.96)(0.30,0.98)(0.35,0.996)(0.40,0.996)(0.45,0.996)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.30)(0.15,0.56)(0.20,0.75)(0.25,0.88)(0.30,0.88)(0.35,0.88)(0.40,0.88)(0.45,0.88)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.06)(0.10,0.08)(0.15,0.11)(0.20,0.18)(0.25,0.25)(0.30,0.35)(0.35,0.51)(0.40,0.68)(0.45,0.80)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.09)(0.10,0.09)(0.15,0.14)(0.20,0.18)(0.25,0.33)(0.30,0.24)(0.35,0.35)(0.40,0.51)(0.45,0.74)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.69)(0.15,0.77)(0.20,0.80)(0.25,0.83)(0.30,0.84)(0.35,0.86)(0.40,0.88)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.15)(0.10,0.16)(0.15,0.17)(0.20,0.18)(0.25,0.16)(0.30,0.18)(0.35,0.23)(0.40,0.19)(0.45,0.25)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-10.2)(3.5,-0.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(E)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.3}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.88)(0.10,0.98)(0.15,0.99)(0.20,0.99)(0.25,0.99)(0.30,0.99)(0.35,0.99)(0.40,0.99)(0.45,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.71)(0.10,0.78)(0.15,0.87)(0.20,0.87)(0.25,0.87)(0.30,0.87)(0.35,0.88)(0.40,0.92)(0.45,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.63)(0.10,0.78)(0.15,0.86)(0.20,0.90)(0.25,0.92)(0.30,0.93)(0.35,0.92)(0.40,0.94)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.56)(0.10,0.69)(0.15,0.73)(0.20,0.73)(0.25,0.76)(0.30,0.76)(0.35,0.80)(0.40,0.86)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.37)(0.10,0.69)(0.15,0.88)(0.20,0.96)(0.25,0.98)(0.30,0.99)(0.35,0.997)(0.40,0.997)(0.45,0.997)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.64)(0.15,0.80)(0.20,0.89)(0.25,0.93)(0.30,0.93)(0.35,0.93)(0.40,0.93)(0.45,0.93)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.34)(0.10,0.50)(0.15,0.64)(0.20,0.85)(0.25,0.90)(0.30,0.95)(0.35,0.96)(0.40,0.96)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.45)(0.10,0.54)(0.15,0.62)(0.20,0.78)(0.25,0.84)(0.30,0.89)(0.35,0.89)(0.40,0.90)(0.45,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.55)(0.10,0.63)(0.15,0.63)(0.20,0.63)(0.25,0.63)(0.30,0.76)(0.35,0.84)(0.40,0.92)(0.45,0.98)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.60)(0.10,0.64)(0.15,0.64)(0.20,0.64)(0.25,0.64)(0.30,0.71)(0.35,0.74)(0.40,0.76)(0.45,0.80)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-8.8)(0.8,1)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(F)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.88)(0.10,0.98)(0.15,0.99)(0.20,0.99)(0.25,0.995)(0.30,0.996)(0.35,0.997)(0.40,0.996)(0.45,0.993)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.69)(0.10,0.79)(0.15,0.81)(0.20,0.82)(0.25,0.91)(0.30,0.92)(0.35,0.92)(0.40,0.92)(0.45,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.33)(0.10,0.47)(0.15,0.64)(0.20,0.74)(0.25,0.79)(0.30,0.81)(0.35,0.91)(0.40,0.88)(0.45,0.91)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.29)(0.10,0.40)(0.15,0.49)(0.20,0.60)(0.25,0.66)(0.30,0.71)(0.35,0.69)(0.40,0.69)(0.45,0.82)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.28)(0.10,0.59)(0.15,0.85)(0.20,0.96)(0.25,0.97)(0.30,0.997)(0.35,0.997)(0.40,0.997)(0.45,0.997)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.26)(0.10,0.46)(0.15,0.64)(0.20,0.86)(0.25,0.89)(0.30,0.89)(0.35,0.89)(0.40,0.89)(0.45,0.89)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.19)(0.10,0.24)(0.15,0.23)(0.20,0.27)(0.25,0.64)(0.30,0.72)(0.35,0.85)(0.40,0.90)(0.45,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.23)(0.15,0.26)(0.20,0.34)(0.25,0.50)(0.30,0.54)(0.35,0.69)(0.40,0.79)(0.45,0.81)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.62)(0.15,0.66)(0.20,0.67)(0.25,0.68)(0.30,0.72)(0.35,0.77)(0.40,0.85)(0.45,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.26)(0.10,0.29)(0.15,0.32)(0.20,0.33)(0.25,0.29)(0.30,0.34)(0.35,0.42)(0.40,0.44)(0.45,0.45)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 7 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-9.2)(3.5,1.2)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(G)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.105)(0.15,0.136)(0.20,0.21)(0.25,0.331)(0.30,0.471)(0.35,0.632)(0.40,0.854)(0.45,0.958)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.101)(0.10,0.124)(0.15,0.181)(0.20,0.261)(0.25,0.384)(0.30,0.469)(0.35,0.588)(0.40,0.756)(0.45,0.867)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.092)(0.10,0.10)(0.15,0.105)(0.20,0.109)(0.25,0.137)(0.30,0.163)(0.35,0.223)(0.40,0.396)(0.45,0.659)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.097)(0.10,0.101)(0.15,0.19)(0.20,0.124)(0.25,0.143)(0.30,0.275)(0.35,0.344)(0.40,0.376)(0.45,0.63)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.101)(0.20,0.108)(0.25,0.143)(0.30,0.241)(0.35,0.449)(0.40,0.719)(0.45,0.863)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.098)(0.10,0.10)(0.15,0.105)(0.20,0.119)(0.25,0.149)(0.30,0.216)(0.35,0.341)(0.40,0.543)(0.45,0.797)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.10)(0.20,0.10)(0.25,0.106)(0.30,0.106)(0.35,0.126)(0.40,0.208)(0.45,0.126)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.098)(0.10,0.10)(0.15,0.10)(0.20,0.102)(0.25,0.107)(0.30,0.11)(0.35,0.147)(0.40,0.244)(0.45,0.473)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.113)(0.15,0.143)(0.20,0.177)(0.25,0.244)(0.30,0.356)(0.35,0.437)(0.40,0.596)(0.45,0.769)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.103)(0.15,0.104)(0.20,0.106)(0.25,0.117)(0.30,0.14)(0.35,0.158)(0.40,0.183)(0.45,0.253)
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 8 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-13.2)(3.5,-3.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(H)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.3}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.493)(0.10,0.512)(0.15,0.589)(0.20,0.762)(0.25,0.898)(0.30,0.966)(0.35,0.982)(0.40,0.991)(0.45,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.502)(0.10,0.536)(0.15,0.619)(0.20,0.746)(0.25,0.805)(0.30,0.861)(0.35,0.912)(0.40,0.937)(0.45,0.958)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.489)(0.10,0.501)(0.15,0.525)(0.20,0.569)(0.25,0.683)(0.30,0.747)(0.35,0.868)(0.40,0.938)(0.45,0.986)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.51)(0.15,0.54)(0.20,0.586)(0.25,0.679)(0.30,0.724)(0.35,0.785)(0.40,0.869)(0.45,0.922)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.501)(0.20,0.512)(0.25,0.542)(0.30,0.615)(0.35,0.742)(0.40,0.893)(0.45,0.976)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.505)(0.20,0.518)(0.25,0.543)(0.30,0.601)(0.35,0.689)(0.40,0.811)(0.45,0.938)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.507)(0.20,0.521)(0.25,0.544)(0.30,0.578)(0.35,0.756)(0.40,0.89)(0.45,0.756)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.504)(0.15,0.51)(0.20,0.527)(0.25,0.556)(0.30,0.596)(0.35,0.703)(0.40,0.788)(0.45,0.903)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.347)(0.10,0.364)(0.15,0.39)(0.20,0.435)(0.25,0.494)(0.30,0.669)(0.35,0.777)(0.40,0.905)(0.45,0.971)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.506)(0.15,0.519)(0.20,0.535)(0.25,0.567)(0.30,0.637)(0.35,0.656)(0.40,0.706)(0.45,0.773)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 9 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-10.8)(0.8,-1)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(I)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.201)(0.10,0.217)(0.15,0.329)(0.20,0.563)(0.25,0.772)(0.30,0.902)(0.35,0.965)(0.40,0.982)(0.45,0.995)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.202)(0.10,0.253)(0.15,0.386)(0.20,0.543)(0.25,0.674)(0.30,0.771)(0.35,0.862)(0.40,0.919)(0.45,0.952)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.201)(0.15,0.207)(0.20,0.228)(0.25,0.277)(0.30,0.352)(0.35,0.524)(0.40,0.692)(0.45,0.836)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.208)(0.15,0.224)(0.20,0.255)(0.25,0.373)(0.30,0.412)(0.35,0.465)(0.40,0.606)(0.45,0.726)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.203)(0.20,0.216)(0.25,0.262)(0.30,0.366)(0.35,0.583)(0.40,0.824)(0.45,0.961)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.206)(0.20,0.22)(0.25,0.254)(0.30,0.319)(0.35,0.456)(0.40,0.644)(0.45,0.884)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.207)(0.25,0.227)(0.30,0.241)(0.35,0.31)(0.40,0.533)(0.45,0.31)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.203)(0.20,0.21)(0.25,0.218)(0.30,0.238)(0.35,0.318)(0.40,0.476)(0.45,0.73)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.219)(0.15,0.262)(0.20,0.312)(0.25,0.399)(0.30,0.519)(0.35,0.626)(0.40,0.789)(0.45,0.926)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.204)(0.15,0.21)(0.20,0.219)(0.25,0.234)(0.30,0.277)(0.35,0.334)(0.40,0.373)(0.45,0.394)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 10 of figure starts
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-11)(3.5,-0.6)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0,Dx=0.05,Dy=0.1](0.42,1.05)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(J)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,1.05)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.14){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,1.07){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,0}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.11)(0.15,0.14)(0.20,0.22)(0.25,0.36)(0.30,0.49)(0.35,0.65)(0.40,0.85)(0.45,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.12)(0.15,0.18)(0.20,0.26)(0.25,0.36)(0.30,0.46)(0.35,0.58)(0.40,0.72)(0.45,0.86)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.101)(0.20,0.112)(0.25,0.141)(0.30,0.165)(0.35,0.224)(0.40,0.355)(0.45,0.632)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.184)(0.15,0.111)(0.20,0.20)(0.25,0.144)(0.30,0.24)(0.35,0.30)(0.40,0.397)(0.45,0.582)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.10)(0.20,0.105)(0.25,0.11)(0.30,0.129)(0.35,0.163)(0.40,0.264)(0.45,0.649)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.102)(0.20,0.106)(0.25,0.116)(0.30,0.132)(0.35,0.161)(0.40,0.239)(0.45,0.536)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.102)(0.20,0.107)(0.25,0.114)(0.30,0.118)(0.35,0.121)(0.40,0.165)(0.45,0.629)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.10)(0.15,0.102)(0.20,0.106)(0.25,0.109)(0.30,0.117)(0.35,0.136)(0.40,0.183)(0.45,0.478)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.112)(0.15,0.133)(0.20,0.186)(0.25,0.258)(0.30,0.35)(0.35,0.434)(0.40,0.566)(0.45,0.778)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.10)(0.10,0.102)(0.15,0.108)(0.20,0.112)(0.25,0.12)(0.30,0.141)(0.35,0.163)(0.40,0.182)(0.45,0.21)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 11 of figure starts
\hspace*{1.5in}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(1.5,-16.2)(3.5,-6.4)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.3,Dx=0.05,Dy=0.1](0.42,0.75)
\rput[mr](-0.07,0.35){$\pmb{\xi}$}
\rput(0.2,-0.2){(K)}
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.75)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.75)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,0.84){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.77){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.3}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.52)(0.15,0.63)(0.20,0.796)(0.25,0.906)(0.30,0.952)(0.35,0.982)(0.40,0.993)(0.45,0.999)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.502)(0.10,0.554)(0.15,0.646)(0.20,0.749)(0.25,0.818)(0.30,0.869)(0.35,0.907)(0.40,0.94)(0.45,0.966)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.502)(0.15,0.529)(0.20,0.615)(0.25,0.701)(0.30,0.765)(0.35,0.85)(0.40,0.921)(0.45,0.978)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, randpm, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.514)(0.15,0.553)(0.20,0.611)(0.25,0.661)(0.30,0.745)(0.35,0.792)(0.40,0.866)(0.45,0.925)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.50)(0.20,0.504)(0.25,0.507)(0.30,0.52)(0.35,0.543)(0.40,0.613)(0.45,0.857)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.50)(0.15,0.502)(0.20,0.505)(0.25,0.513)(0.30,0.522)(0.35,0.547)(0.40,0.607)(0.45,0.797)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.501)(0.10,0.507)(0.15,0.511)(0.20,0.514)(0.25,0.535)(0.30,0.62)(0.35,0.678)(0.40,0.82)(0.45,0.903)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.502)(0.10,0.508)(0.15,0.51)(0.20,0.513)(0.25,0.542)(0.30,0.57)(0.35,0.69)(0.40,0.767)(0.45,0.81)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.331)(0.10,0.351)(0.15,0.376)(0.20,0.444)(0.25,0.505)(0.30,0.667)(0.35,0.776)(0.40,0.882)(0.45,0.972)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.50)(0.10,0.507)(0.15,0.515)(0.20,0.539)(0.25,0.57)(0.30,0.62)(0.35,0.666)(0.40,0.706)(0.45,0.761)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%
\hspace*{0.95in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 12 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
\subfigure{
\scalebox{0.7}[0.50]{
\begin{pspicture}(-0.8,-12.8)(0.8,-3)
\psset{xunit=5.5in,yunit=2.5in}
%
\def\pshlabel#1{\scalebox{0.9}{\footnotesize\bf #1}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1pt,Ox=0.05,Oy=0.1,Dx=0.05,Dy=0.1](0.42,0.95)
%
%%%%%%% grid follows
%
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(0.42,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(0.42,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(0.42,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(0.42,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(0.42,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(0.42,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(0.42,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(0.42,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(0.42,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(0.42,1.00)
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.00)(0.05,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.10,0.00)(0.10,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.15,0.00)(0.15,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.20,0.00)(0.20,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.25,0.00)(0.25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.30,0.00)(0.30,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.35,0.00)(0.35,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0.40,0.00)(0.40,0.95)
%
%%%%%%% gamma label for x axis
%
\rput[mr](-0.03,-0.07){$\scriptstyle\pmb{\Phi\,-\,\gamma}$}
\rput[mr](-0.03,-0.12){$\scriptstyle\pmb{\gamma}$}
\rput(0.00,-0.12){\scalebox{0.9}{\bf\footnotesize 0.45}}
\rput(0.05,-0.12){\scalebox{0.9}{\bf\footnotesize 0.40}}
\rput(0.10,-0.12){\scalebox{0.9}{\bf\footnotesize 0.35}}
\rput(0.15,-0.12){\scalebox{0.9}{\bf\footnotesize 0.30}}
\rput(0.20,-0.12){\scalebox{0.9}{\bf\footnotesize 0.25}}
\rput(0.25,-0.12){\scalebox{0.9}{\bf\footnotesize 0.20}}
\rput(0.30,-0.12){\scalebox{0.9}{\bf\footnotesize 0.15}}
\rput(0.35,-0.12){\scalebox{0.9}{\bf\footnotesize 0.10}}
\rput(0.40,-0.12){\scalebox{0.9}{\bf\footnotesize 0.05}}
%
\rput[mr](-0.07,0.45){$\pmb{\xi}$}
\rput(0.2,-0.2){(L)}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput(0.2,1.04){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput(0.2,0.97){\footnotesize $\pmb{E=|V|=300}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.9}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$}
%
\psset{origin={-0.05,-0.1}}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.225)(0.15,0.36)(0.20,0.572)(0.25,0.77)(0.30,0.891)(0.35,0.953)(0.40,0.987)(0.45,0.997)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.202)(0.10,0.266)(0.15,0.39)(0.20,0.544)(0.25,0.664)(0.30,0.763)(0.35,0.838)(0.40,0.889)(0.45,0.927)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.211)(0.20,0.235)(0.25,0.284)(0.30,0.371)(0.35,0.482)(0.40,0.676)(0.45,0.858)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.274)(0.15,0.278)(0.20,0.254)(0.25,0.344)(0.30,0.39)(0.35,0.485)(0.40,0.622)(0.45,0.743)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.20)(0.20,0.205)(0.25,0.211)(0.30,0.23)(0.35,0.265)(0.40,0.368)(0.45,0.756)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.20)(0.15,0.202)(0.20,0.206)(0.25,0.216)(0.30,0.232)(0.35,0.262)(0.40,0.341)(0.45,0.628)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.202)(0.15,0.21)(0.20,0.214)(0.25,0.217)(0.30,0.23)(0.35,0.294)(0.40,0.567)(0.45,0.816)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.202)(0.15,0.207)(0.20,0.213)(0.25,0.215)(0.30,0.226)(0.35,0.277)(0.40,0.472)(0.45,0.70)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.225)(0.15,0.26)(0.20,0.337)(0.25,0.417)(0.30,0.536)(0.35,0.642)(0.40,0.781)(0.45,0.93)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](0.05,0.20)(0.10,0.206)(0.15,0.209)(0.20,0.226)(0.25,0.241)(0.30,0.282)(0.35,0.325)(0.40,0.321)(0.45,0.393)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
\vspace*{-2.0in}
\caption{\label{newfig3-full}Effect of variations of equity to asset ratio (with respect to shock) on the vulnerability index $\xi$ for 
$(\alpha,\beta)$-heterogeneous networks. Lower values of $\xi$ imply higher global stability of a network.
}
%
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%














\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig4-coordinated-and-random
%%%\input{../tex-figures/newfig4-coordinated-and-random.tex}

\begin{figure*}
%
\vspace*{1.2in}
\hspace*{-0.5in}
%
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-3,-7.5)(-1,9.5)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}
%
%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[mr](5,-7.5){\LARGE\bf (A)}
%
\psline[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](7.50,16.2)(8.5,16.2)
\rput[mr](7.35,16.2){\Large\bf {\sf ER} model (average degree $\pmb{6}$), coordinated shock}
\psline[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](25.65,16.2)(26.65,16.2)
\rput[mr](25.55,16.2){\Large\bf {\sf ER} model (average degree $\pmb{3}$), coordinated shock}
%%
\psline[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](17.20,15.3)(18.20,15.3)
\rput[mr](17.05,15.3){\Large\bf {\sf ER} model (average degree $\pmb{6}$), idiosyncratic shock}
\psline[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](35.55,15.3)(36.55,15.3)
\rput[mr](35.05,15.3){\Large\bf {\sf ER} model (average degree $\pmb{3}$), idiosyncratic shock}
%%
\psline[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](7.50,14.4)(8.5,14.4)
\rput[mr](7.35,14.4){\Large\bf {\sf SF} model (average degree $\pmb{6}$), coordinated shock}
\psline[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](25.65,14.4)(26.65,14.4)
\rput[mr](25.55,14.4){\Large\bf {\sf SF} model (average degree $\pmb{3}$), coordinated shock}
%%
\psline[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](17.20,13.5)(18.20,13.5)
\rput[mr](17.05,13.5){\Large\bf {\sf SF} model (average degree $\pmb{6}$), idiosyncratic shock}
\psline[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](35.55,13.5)(36.55,13.5)
\rput[mr](35.05,13.5){\Large\bf {\sf SF} model (average degree $\pmb{3}$), idiosyncratic shock}
%%
\psline[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](10,12.5)(11,12.5)
\rput[mr](9.85,12.5){\Large\bf in-arborescence (average degree $\pmb{\approx 1}$), coordinated shock}
%%
\psline[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](29.95,12.5)(30.95,12.5)
\rput[mr](29.85,12.5){\Large\bf in-arborescence (average degree $\pmb{\approx 1}$), idiosyncratic shock}
%
\rput[ml](1,11.0){\Large$\pmb{n=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,01.06)(1,2,01.06)(1,3,01.06)(1,4,01.36)(1,5,01.36)(1,6,01.36)(1,7,01.36)(1,8,01.64)(1,9,01.64)(1,10,01.64)(1,11,01.64)(1,12,01.88)(1,13,01.88)(1,14,01.88)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.14)(5,2,00.14)(5,3,00.14)(5,4,00.2)(5,5,00.2)(5,6,00.2)(5,7,00.2)(5,8,00.3)(5,9,00.3)(5,10,00.3)(5,11,00.3)(5,12,00.3)(5,13,00.3)(5,14,00.3)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.02)(9,2,00.02)(9,3,00.02)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,02.9)(1,2,02.9)(1,3,02.9)(1,4,03.14)(1,5,03.14)(1,6,03.14)(1,7,03.14)(1,8,03.62)(1,9,03.62)(1,10,03.62)(1,11,03.62)(1,12,04.02)(1,13,04.02)(1,14,04.02)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,00.58)(5,2,00.58)(5,3,00.58)(5,4,00.4)(5,5,00.4)(5,6,00.4)(5,7,00.4)(5,8,00.52)(5,9,00.52)(5,10,00.52)(5,11,00.52)(5,12,00.58)(5,13,00.58)(5,14,00.58)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.34)(9,2,00.34)(9,3,00.34)(9,4,00.04)(9,5,00.04)(9,6,00.04)(9,7,00.04)(9,8,00.04)(9,9,00.04)(9,10,00.04)(9,11,00.04)(9,12,00.04)(9,13,00.04)(9,14,00.04)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,01.82)(1,2,01.76)(1,3,01.12)(1,4,01.18)(1,5,03.56)(1,6,01.86)(1,7,02.84)(1,8,04.3)(1,9,02.0)(1,10,02.88)(1,11,02.16)(1,12,03.96)(1,13,03.56)(1,14,04.66)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.06)(5,2,00.12)(5,3,00.18)(5,4,00.14)(5,5,00.16)(5,6,00.12)(5,7,00.22)(5,8,00.2)(5,9,00.24)(5,10,00.36)(5,11,00.26)(5,12,00.38)(5,13,00.28)(5,14,00.36)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.02)(9,2,00.02)(9,3,00.02)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,06.8)(1,2,05.72)(1,3,04.44)(1,4,06.76)(1,5,04.66)(1,6,04.12)(1,7,06.28)(1,8,08.18)(1,9,0.624)(1,10,07.04)(1,11,05.3)(1,12,06.32)(1,13,06.84)(1,14,07.28)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,00.5)(5,2,00.42)(5,3,00.56)(5,4,00.26)(5,5,00.38)(5,6,00.44)(5,7,00.34)(5,8,01.44)(5,9,00.52)(5,10,00.42)(5,11,01.5)(5,12,00.54)(5,13,00.62)(5,14,00.6)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.34)(9,2,00.34)(9,3,00.36)(9,4,00.06)(9,5,00.02)(9,6,00.02)(9,7,00.02)(9,8,00.02)(9,9,00.04)(9,10,00.08)(9,11,00.04)(9,12,00.02)(9,13,00.1)(9,14,00.04)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,07.22)(1,2,07.22)(1,3,07.22)(1,4,06.92)(1,5,06.92)(1,6,06.92)(1,7,06.92)(1,8,06.66)(1,9,06.66)(1,10,06.66)(1,11,06.66)(1,12,06.48)(1,13,06.48)(1,14,06.48)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.06)(5,2,00.06)(5,3,00.06)(5,4,00.04)(5,5,00.04)(5,6,00.04)(5,7,00.04)(5,8,00.06)(5,9,00.06)(5,10,00.06)(5,11,00.06)(5,12,00.06)(5,13,00.06)(5,14,00.06)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.02)(9,2,00.02)(9,3,00.02)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,08.84)(1,2,08.84)(1,3,08.84)(1,4,08.54)(1,5,08.54)(1,6,08.54)(1,7,08.54)(1,8,08.02)(1,9,08.02)(1,10,08.02)(1,11,08.02)(1,12,07.14)(1,13,07.14)(1,14,07.14)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,01.14)(5,2,01.14)(5,3,01.14)(5,4,00.26)(5,5,00.26)(5,6,00.26)(5,7,00.26)(5,8,00.18)(5,9,00.18)(5,10,00.18)(5,11,00.18)(5,12,00.22)(5,13,00.22)(5,14,00.22)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,00.72)(9,2,00.72)(9,3,00.72)(9,4,00.06)(9,5,00.06)(9,6,00.06)(9,7,00.06)(9,8,00.06)(9,9,00.06)(9,10,00.06)(9,11,00.06)(9,12,00.06)(9,13,00.06)(9,14,00.06)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,02.28)(1,2,01.4)(1,3,01.46)(1,4,01.52)(1,5,00.7)(1,6,02.54)(1,7,01.72)(1,8,01.84)(1,9,01.76)(1,10,00.72)(1,11,01.82)(1,12,02.88)(1,13,02.88)(1,14,00.94)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,00.14)(5,2,00.14)(5,3,00.18)(5,4,00.2)(5,5,00.16)(5,6,00.18)(5,7,00.22)(5,8,00.36)(5,9,00.36)(5,10,00.36)(5,11,00.3)(5,12,00.5)(5,13,00.4)(5,14,00.4)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.002)(9,3,0.002)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,03.26)(1,2,01.92)(1,3,02.22)(1,4,02.46)(1,5,04.66)(1,6,02.52)(1,7,02.96)(1,8,03.26)(1,9,03.18)(1,10,02.7)(1,11,04.68)(1,12,02.86)(1,13,04.14)(1,14,04.3)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,01.02)(5,2,00.8)(5,3,00.96)(5,4,00.42)(5,5,00.3)(5,6,00.48)(5,7,00.42)(5,8,00.56)(5,9,00.6)(5,10,00.54)(5,11,00.46)(5,12,00.8)(5,13,00.66)(5,14,00.68)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.66)(9,2,00.68)(9,3,00.74)(9,4,00.02)(9,5,00.04)(9,6,00.08)(9,7,00.1)(9,8,00.04)(9,9,00.16)(9,10,00.06)(9,11,00.16)(9,12,00.06)(9,13,00.08)(9,14,00.08)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,09.38)(1,2,09.38)(1,3,09.38)(1,4,07.4)(1,5,07.4)(1,6,07.4)(1,7,07.4)(1,8,06.96)(1,9,06.96)(1,10,06.96)(1,11,06.96)(1,12,06.78)(1,13,06.78)(1,14,06.78)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,07.58)(5,2,07.58)(5,3,07.58)(5,4,01.84)(5,5,01.84)(5,6,01.84)(5,7,01.84)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,06.62)(9,2,06.62)(9,3,06.62)(9,4,00.3)(9,5,00.3)(9,6,00.3)(9,7,00.3)(9,8,00.3)(9,9,00.3)(9,10,00.3)(9,11,00.3)(9,12,00.34)(9,13,00.34)(9,14,00.34)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,06.32)(1,2,06.58)(1,3,06.52)(1,4,01.2)(1,5,01.4)(1,6,01.74)(1,7,01.74)(1,8,02.78)(1,9,02.18)(1,10,02.66)(1,11,02.62)(1,12,02.08)(1,13,02.26)(1,14,02.66)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,06.12)(5,2,05.84)(5,3,05.78)(5,4,00.26)(5,5,00.36)(5,6,00.68)(5,7,00.48)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,05.8)(9,2,05.68)(9,3,05.74)(9,4,00.04)(9,5,00.04)(9,6,00.0)(9,7,00.0)(9,8,00.02)(9,9,00.06)(9,10,00.0)(9,11,00.0)(9,12,00.02)(9,13,00.02)(9,14,00.06)
%
%\pstThreeDPut(1,1,8){haha}
%
%%\savedata{\mydata}[
%%{
%%(1,1,0.00)(1,2,0.02)(1,3,0.06)(1,4,0.12)(1,5,0.2)(1,6,0.3)(1,7,0.34)(1,8,0.56)(1,9,1.36)
%%%(2,1,0.00)(2,2,0.02)(2,3,0.06)(2,4,0.12)(2,5,0.2)(2,6,0.3)(2,7,0.34)(2,8,0.56)(2,9,1.36)
%%}
%%]
%%\dataplotThreeD[plotstyle=line,fillstyle=solid,fillcolor=red,gradbegin=red,gradmidpoint=0.5,linewidth=1pt]{\mydata}
%%%
%%\savedata{\mydata}[
%%{
%%(2,1,0.00)(2,2,0.02)(2,3,0.06)(2,4,0.12)(2,5,0.2)(2,6,0.3)(2,7,0.34)(2,8,0.56)(2,9,1.36)
%%}
%%]
%%\dataplotThreeD[plotstyle=line,fillstyle=solid,fillcolor=blue,gradbegin=red,gradmidpoint=0.5,linewidth=1pt]{\mydata}
%
%\savedata{\newdata}[{2,2,9}, {1,1,1}, {5,5,5}, {6,6,6}, {7,7,7}]
%\dataplotThreeD[plotstyle=curve,fillstyle=solid,fillcolor=blue,gradbegin=blue,gradmidpoint=0.5,linewidth=0pt]{\newdata}
%%%%%%%%%%%%%%%%%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%%%%%%%%%%%%%%%%%
\end{pspicture}
}
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% part 2 of figure starts
%
\hspace*{1.7in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-4,-7.5)(-2,9.5)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}

%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
\rput[ml](1,11.0){\Large$\pmb{n=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
\rput[mr](5,-7.5){\LARGE\bf (B)}
%
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,05.03)(1,2,05.03)(1,3,05.03)(1,4,06.70)(1,5,06.70)(1,6,06.70)(1,7,06.70)(1,8,07.90)(1,9,07.90)(1,10,07.90)(1,11,07.90)(1,12,09.00)(1,13,09.00)(1,14,09.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.80)(5,2,00.80)(5,3,00.80)(5,4,01.0)(5,5,01.0)(5,6,01.0)(5,7,01.0)(5,8,01.4)(5,9,01.4)(5,10,01.4)(5,11,01.4)(5,12,01.7)(5,13,01.7)(5,14,01.7)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,05.8)(1,2,05.8)(1,3,05.8)(1,4,07.50)(1,5,07.50)(1,6,07.50)(1,7,07.50)(1,8,08.70)(1,9,08.70)(1,10,08.70)(1,11,08.70)(1,12,09.20)(1,13,09.20)(1,14,09.20)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,01.60)(5,2,01.60)(5,3,01.60)(5,4,01.7)(5,5,01.7)(5,6,01.7)(5,7,01.7)(5,8,02.50)(5,9,02.50)(5,10,02.50)(5,11,02.50)(5,12,03.60)(5,13,03.60)(5,14,03.60)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.40)(9,2,00.40)(9,3,00.40)(9,4,00.10)(9,5,00.10)(9,6,00.10)(9,7,00.10)(9,8,00.10)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.20)(9,13,00.20)(9,14,00.20)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,07.20)(1,2,08.20)(1,3,04.60)(1,4,09.00)(1,5,07.80)(1,6,07.40)(1,7,07.20)(1,8,09.0)(1,9,08.8)(1,10,08.00)(1,11,08.60)(1,12,09.20)(1,13,08.60)(1,14,08.90)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.60)(5,2,00.60)(5,3,00.70)(5,4,00.80)(5,5,01.00)(5,6,00.80)(5,7,00.90)(5,8,01.3)(5,9,01.60)(5,10,01.40)(5,11,01.50)(5,12,01.90)(5,13,01.60)(5,14,02.00)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,06.7)(1,2,06.70)(1,3,07.60)(1,4,08.30)(1,5,07.20)(1,6,07.80)(1,7,08.10)(1,8,08.90)(1,9,9.000)(1,10,09.10)(1,11,08.8)(1,12,09.00)(1,13,09.00)(1,14,09.20)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,01.6)(5,2,01.40)(5,3,01.30)(5,4,01.80)(5,5,01.80)(5,6,02.60)(5,7,01.70)(5,8,02.60)(5,9,03.10)(5,10,02.50)(5,11,02.4)(5,12,03.20)(5,13,03.30)(5,14,03.7)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.50)(9,2,00.40)(9,3,00.40)(9,4,00.20)(9,5,00.20)(9,6,00.30)(9,7,00.30)(9,8,00.30)(9,9,00.30)(9,10,00.30)(9,11,00.20)(9,12,00.20)(9,13,00.2)(9,14,00.30)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,09.60)(1,2,09.60)(1,3,09.60)(1,4,07.80)(1,5,07.80)(1,6,07.80)(1,7,07.80)(1,8,08.40)(1,9,08.40)(1,10,08.40)(1,11,08.40)(1,12,08.10)(1,13,08.10)(1,14,08.10)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.60)(5,2,00.60)(5,3,00.60)(5,4,00.90)(5,5,00.90)(5,6,00.90)(5,7,00.90)(5,8,01.40)(5,9,01.40)(5,10,01.40)(5,11,01.40)(5,12,01.90)(5,13,01.90)(5,14,01.90)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,08.60)(1,2,08.60)(1,3,08.60)(1,4,08.70)(1,5,08.70)(1,6,08.70)(1,7,08.70)(1,8,08.70)(1,9,08.70)(1,10,08.70)(1,11,08.70)(1,12,08.70)(1,13,08.70)(1,14,08.70)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,02.60)(5,2,02.60)(5,3,02.60)(5,4,02.20)(5,5,02.20)(5,6,02.20)(5,7,02.20)(5,8,03.90)(5,9,03.90)(5,10,03.90)(5,11,03.90)(5,12,03.70)(5,13,03.70)(5,14,03.70)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,01.10)(9,2,01.10)(9,3,01.10)(9,4,00.40)(9,5,00.40)(9,6,00.40)(9,7,00.40)(9,8,00.40)(9,9,00.40)(9,10,00.40)(9,11,00.40)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,08.00)(1,2,08.1)(1,3,06.70)(1,4,05.90)(1,5,05.9)(1,6,06.10)(1,7,07.00)(1,8,07.10)(1,9,07.10)(1,10,06.90)(1,11,06.90)(1,12,08.00)(1,13,08.30)(1,14,07.80)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,01.00)(5,2,00.80)(5,3,00.70)(5,4,01.2)(5,5,01.00)(5,6,01.30)(5,7,01.30)(5,8,01.70)(5,9,01.60)(5,10,01.70)(5,11,01.7)(5,12,02.2)(5,13,02.1)(5,14,02.2)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.000)(9,3,0.000)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,06.40)(1,2,07.40)(1,3,06.90)(1,4,07.60)(1,5,06.70)(1,6,07.90)(1,7,06.60)(1,8,08.10)(1,9,08.30)(1,10,08.8)(1,11,08.50)(1,12,08.80)(1,13,08.90)(1,14,08.7)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,02.20)(5,2,03.5)(5,3,02.30)(5,4,01.80)(5,5,02.1)(5,6,02.80)(5,7,02.00)(5,8,03.20)(5,9,03.4)(5,10,04.00)(5,11,03.90)(5,12,03.8)(5,13,03.80)(5,14,03.60)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.70)(9,2,00.70)(9,3,00.70)(9,4,00.30)(9,5,00.30)(9,6,00.50)(9,7,00.4)(9,8,00.30)(9,9,00.40)(9,10,00.30)(9,11,00.40)(9,12,00.30)(9,13,00.40)(9,14,00.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,10.00)(1,2,10.00)(1,3,10.00)(1,4,10.0)(1,5,10.0)(1,6,10.0)(1,7,10.0)(1,8,10.00)(1,9,10.00)(1,10,10.00)(1,11,10.00)(1,12,10.00)(1,13,10.00)(1,14,10.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,08.50)(5,2,08.50)(5,3,08.50)(5,4,04.50)(5,5,04.50)(5,6,04.50)(5,7,04.50)(5,8,03.7)(5,9,03.7)(5,10,03.7)(5,11,03.7)(5,12,03.7)(5,13,03.7)(5,14,03.7)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,06.60)(9,2,06.60)(9,3,06.60)(9,4,00.3)(9,5,00.3)(9,6,00.3)(9,7,00.3)(9,8,00.3)(9,9,00.3)(9,10,00.3)(9,11,00.3)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,05.80)(1,2,06.10)(1,3,05.80)(1,4,07.6)(1,5,06.8)(1,6,07.00)(1,7,07.30)(1,8,07.90)(1,9,08.30)(1,10,07.90)(1,11,08.20)(1,12,07.50)(1,13,08.70)(1,14,08.20)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,04.30)(5,2,04.10)(5,3,04.40)(5,4,02.10)(5,5,02.20)(5,6,02.50)(5,7,02.00)(5,8,05.0)(5,9,05.0)(5,10,05.0)(5,11,05.0)(5,12,05.0)(5,13,05.0)(5,14,05.0)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,03.4)(9,2,03.30)(9,3,03.30)(9,4,00.10)(9,5,00.20)(9,6,00.2)(9,7,00.1)(9,8,00.20)(9,9,00.20)(9,10,00.2)(9,11,00.2)(9,12,00.30)(9,13,00.20)(9,14,00.10)
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}
%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%
\end{pspicture}
}
%
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% part 3 of figure starts
%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\hspace*{-0.0in}
%
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-3,-7)(-1.95,13)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}

%
%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
\rput[ml](1,11.0){\Large$\pmb{n=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
\rput[mr](5,-7.5){\LARGE\bf (C)}
%
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,01.20)(1,2,01.20)(1,3,01.20)(1,4,01.40)(1,5,01.40)(1,6,01.40)(1,7,01.40)(1,8,01.60)(1,9,01.60)(1,10,01.60)(1,11,01.60)(1,12,01.90)(1,13,01.90)(1,14,01.90)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.20)(5,2,00.20)(5,3,00.20)(5,4,00.2)(5,5,00.2)(5,6,00.2)(5,7,00.2)(5,8,00.3)(5,9,00.3)(5,10,00.3)(5,11,00.3)(5,12,00.3)(5,13,00.3)(5,14,00.3)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,02.3)(1,2,02.3)(1,3,02.3)(1,4,02.30)(1,5,02.30)(1,6,02.30)(1,7,02.30)(1,8,03.00)(1,9,03.00)(1,10,03.00)(1,11,03.00)(1,12,03.30)(1,13,03.30)(1,14,03.30)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,00.70)(5,2,00.70)(5,3,00.70)(5,4,00.4)(5,5,00.4)(5,6,00.4)(5,7,00.4)(5,8,00.50)(5,9,00.50)(5,10,00.50)(5,11,00.50)(5,12,00.60)(5,13,00.60)(5,14,00.60)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.50)(9,2,00.50)(9,3,00.50)(9,4,00.10)(9,5,00.10)(9,6,00.10)(9,7,00.10)(9,8,00.10)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.10)(9,13,00.10)(9,14,00.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,02.90)(1,2,01.00)(1,3,01.90)(1,4,01.50)(1,5,03.00)(1,6,02.20)(1,7,01.20)(1,8,02.9)(1,9,03.4)(1,10,02.40)(1,11,01.40)(1,12,03.30)(1,13,04.00)(1,14,03.00)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.10)(5,2,00.10)(5,3,00.10)(5,4,00.20)(5,5,00.20)(5,6,00.20)(5,7,00.20)(5,8,00.2)(5,9,00.30)(5,10,00.30)(5,11,00.30)(5,12,00.30)(5,13,00.40)(5,14,00.40)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,07.4)(1,2,08.10)(1,3,09.00)(1,4,06.80)(1,5,06.70)(1,6,05.90)(1,7,06.80)(1,8,05.80)(1,9,7.300)(1,10,07.20)(1,11,07.7)(1,12,08.20)(1,13,07.00)(1,14,07.90)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,00.7)(5,2,00.80)(5,3,00.60)(5,4,00.40)(5,5,00.30)(5,6,00.30)(5,7,00.40)(5,8,00.50)(5,9,00.40)(5,10,00.50)(5,11,00.5)(5,12,01.50)(5,13,00.60)(5,14,00.6)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.40)(9,2,00.50)(9,3,00.40)(9,4,00.00)(9,5,00.10)(9,6,00.00)(9,7,00.00)(9,8,00.00)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.10)(9,13,00.1)(9,14,00.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,09.60)(1,2,09.60)(1,3,09.60)(1,4,07.10)(1,5,07.10)(1,6,07.10)(1,7,07.10)(1,8,06.20)(1,9,06.20)(1,10,06.20)(1,11,06.20)(1,12,07.00)(1,13,07.00)(1,14,07.00)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.10)(5,2,00.10)(5,3,00.10)(5,4,00.10)(5,5,00.10)(5,6,00.10)(5,7,00.10)(5,8,00.10)(5,9,00.10)(5,10,00.10)(5,11,00.10)(5,12,00.10)(5,13,00.10)(5,14,00.10)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,07.60)(1,2,07.60)(1,3,07.60)(1,4,07.00)(1,5,07.00)(1,6,07.00)(1,7,07.00)(1,8,06.30)(1,9,06.30)(1,10,06.30)(1,11,06.30)(1,12,05.80)(1,13,05.80)(1,14,05.80)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,01.20)(5,2,01.20)(5,3,01.20)(5,4,00.40)(5,5,00.40)(5,6,00.40)(5,7,00.40)(5,8,00.30)(5,9,00.30)(5,10,00.30)(5,11,00.30)(5,12,00.30)(5,13,00.30)(5,14,00.30)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,00.90)(9,2,00.90)(9,3,00.90)(9,4,00.00)(9,5,00.00)(9,6,00.00)(9,7,00.00)(9,8,00.00)(9,9,00.00)(9,10,00.00)(9,11,00.00)(9,12,00.00)(9,13,00.00)(9,14,00.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,03.10)(1,2,04.2)(1,3,01.50)(1,4,03.40)(1,5,00.8)(1,6,01.60)(1,7,02.40)(1,8,01.70)(1,9,02.70)(1,10,02.40)(1,11,00.90)(1,12,01.00)(1,13,01.00)(1,14,01.10)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,00.20)(5,2,00.30)(5,3,00.20)(5,4,00.2)(5,5,00.30)(5,6,00.30)(5,7,00.30)(5,8,00.40)(5,9,00.40)(5,10,00.40)(5,11,00.4)(5,12,00.5)(5,13,00.5)(5,14,00.5)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.000)(9,3,0.000)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,02.70)(1,2,02.90)(1,3,03.90)(1,4,03.40)(1,5,03.80)(1,6,01.60)(1,7,03.50)(1,8,01.60)(1,9,04.10)(1,10,01.9)(1,11,02.60)(1,12,02.90)(1,13,01.90)(1,14,04.2)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,01.20)(5,2,01.0)(5,3,01.90)(5,4,00.50)(5,5,00.5)(5,6,00.60)(5,7,00.60)(5,8,01.20)(5,9,00.5)(5,10,00.60)(5,11,01.40)(5,12,00.9)(5,13,00.90)(5,14,00.80)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.90)(9,2,00.90)(9,3,00.80)(9,4,00.10)(9,5,00.10)(9,6,00.10)(9,7,00.1)(9,8,00.20)(9,9,00.10)(9,10,00.10)(9,11,00.10)(9,12,00.10)(9,13,00.10)(9,14,00.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,09.50)(1,2,09.50)(1,3,09.50)(1,4,07.6)(1,5,07.6)(1,6,07.6)(1,7,07.6)(1,8,07.40)(1,9,07.40)(1,10,07.40)(1,11,07.40)(1,12,07.00)(1,13,07.00)(1,14,07.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,07.60)(5,2,07.60)(5,3,07.60)(5,4,01.40)(5,5,01.40)(5,6,01.40)(5,7,01.40)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,07.00)(9,2,07.00)(9,3,07.00)(9,4,00.3)(9,5,00.3)(9,6,00.3)(9,7,00.3)(9,8,00.3)(9,9,00.3)(9,10,00.3)(9,11,00.3)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,06.40)(1,2,06.70)(1,3,06.80)(1,4,02.6)(1,5,01.8)(1,6,01.50)(1,7,02.10)(1,8,01.80)(1,9,02.40)(1,10,02.30)(1,11,02.50)(1,12,02.10)(1,13,02.40)(1,14,02.40)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,06.20)(5,2,06.30)(5,3,06.20)(5,4,00.40)(5,5,00.30)(5,6,00.40)(5,7,00.40)(5,8,01.0)(5,9,01.0)(5,10,01.0)(5,11,01.0)(5,12,01.0)(5,13,01.0)(5,14,01.0)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,06.0)(9,2,06.10)(9,3,06.00)(9,4,00.00)(9,5,00.00)(9,6,00.0)(9,7,00.1)(9,8,00.00)(9,9,00.00)(9,10,00.1)(9,11,00.0)(9,12,00.00)(9,13,00.10)(9,14,00.10)
%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%
\end{pspicture}
}
%
\end{minipage}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% part 4 of figure starts
%
\hspace*{1.7in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{minipage}[t]{2in}
\scalebox{0.43}[0.43]{
\begin{pspicture}(-4,-7.5)(-2,9.5)
%
\psset{xunit=0.4in,yunit=0.4in,runit=0.4in}
\psset{nameX=\LARGE$\pmb{\gamma}$,nameY=\LARGE$\pmb{E}$,nameZ=\LARGE$\pmb{\xi}$}
\psset{coorType=1,Alpha=135,hiddenLine=true}

%%\pstThreeDPlaneGrid[planeGrid=xy,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%%\pstThreeDPlaneGrid[planeGridOffset=10,linewidth=0.1pt,ysubticks=14,xsubticks=9,linecolor=darkgray](0,0)(9,14)
%
%%\pstThreeDPlaneGrid[planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%%\pstThreeDPlaneGrid[planeGridOffset=14,planeGrid=xz,linewidth=1pt,xsubticks=9,ysubticks=10,linecolor=darkgray](0,0)(9,10)
%
%\pstThreeDPlaneGrid[planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=1,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%%\pstThreeDPlaneGrid[planeGridOffset=9,planeGrid=yz,linewidth=0.1pt,xsubticks=14,ysubticks=10,linecolor=darkgray](0,0)(14,10)
%
\rput[ml](1,11.0){\Large$\pmb{n=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05,0.25,0.45}$}
%
\rput[mr](5,-7.5){\LARGE\bf (D)}
%
%
%%%%%%%%%%%%%%%% \gamma=0.05,0.25,0.45
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](1,1,04.80)(1,2,04.80)(1,3,04.80)(1,4,06.70)(1,5,06.70)(1,6,06.70)(1,7,06.70)(1,8,07.90)(1,9,07.90)(1,10,07.90)(1,11,07.90)(1,12,08.90)(1,13,08.90)(1,14,08.90)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.70)(5,2,00.70)(5,3,00.70)(5,4,01.1)(5,5,01.1)(5,6,01.1)(5,7,01.1)(5,8,01.5)(5,9,01.5)(5,10,01.5)(5,11,01.5)(5,12,01.8)(5,13,01.8)(5,14,01.8)
\pstThreeDLine[linewidth=8pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](1,1,06.3)(1,2,06.3)(1,3,06.3)(1,4,07.60)(1,5,07.60)(1,6,07.60)(1,7,07.60)(1,8,08.80)(1,9,08.80)(1,10,08.80)(1,11,08.80)(1,12,09.30)(1,13,09.30)(1,14,09.30)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](5,1,02.00)(5,2,02.00)(5,3,02.00)(5,4,02.2)(5,5,02.2)(5,6,02.2)(5,7,02.2)(5,8,02.70)(5,9,02.70)(5,10,02.70)(5,11,02.70)(5,12,03.20)(5,13,03.20)(5,14,03.20)
\pstThreeDLine[linewidth=8pt,linecolor=red,arrowsize=1.5pt 2](9,1,00.70)(9,2,00.70)(9,3,00.70)(9,4,00.30)(9,5,00.30)(9,6,00.30)(9,7,00.30)(9,8,00.30)(9,9,00.30)(9,10,00.30)(9,11,00.30)(9,12,00.30)(9,13,00.30)(9,14,00.30)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](1,1,07.60)(1,2,08.00)(1,3,06.50)(1,4,06.90)(1,5,08.30)(1,6,08.50)(1,7,08.60)(1,8,08.7)(1,9,08.1)(1,10,08.40)(1,11,08.70)(1,12,09.10)(1,13,09.00)(1,14,09.20)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](5,1,00.70)(5,2,00.70)(5,3,00.70)(5,4,01.00)(5,5,01.00)(5,6,01.00)(5,7,01.20)(5,8,01.4)(5,9,01.40)(5,10,01.40)(5,11,01.30)(5,12,01.70)(5,13,01.80)(5,14,01.70)
\pstThreeDLine[linewidth=2pt,linecolor=black,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.02)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](1,1,07.2)(1,2,07.30)(1,3,07.80)(1,4,08.40)(1,5,08.40)(1,6,07.80)(1,7,08.20)(1,8,08.60)(1,9,8.800)(1,10,09.00)(1,11,08.7)(1,12,09.20)(1,13,09.00)(1,14,09.00)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](5,1,01.7)(5,2,01.60)(5,3,02.40)(5,4,02.00)(5,5,01.90)(5,6,01.90)(5,7,01.90)(5,8,03.90)(5,9,02.50)(5,10,02.50)(5,11,04.0)(5,12,03.00)(5,13,04.40)(5,14,03.6)
\pstThreeDLine[linewidth=2pt,linecolor=gray,arrowsize=1.5pt 2](9,1,00.50)(9,2,00.60)(9,3,00.50)(9,4,00.30)(9,5,00.30)(9,6,00.30)(9,7,00.30)(9,8,00.30)(9,9,00.30)(9,10,00.30)(9,11,00.20)(9,12,00.30)(9,13,00.3)(9,14,00.30)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](1,1,09.40)(1,2,09.40)(1,3,09.40)(1,4,07.10)(1,5,07.10)(1,6,07.10)(1,7,07.10)(1,8,07.90)(1,9,07.90)(1,10,07.90)(1,11,07.90)(1,12,08.00)(1,13,08.00)(1,14,08.00)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](5,1,00.90)(5,2,00.90)(5,3,00.90)(5,4,01.20)(5,5,01.20)(5,6,01.20)(5,7,01.20)(5,8,01.80)(5,9,01.80)(5,10,01.80)(5,11,01.80)(5,12,02.40)(5,13,02.40)(5,14,02.40)
\pstThreeDLine[linewidth=8pt,linecolor=yellow,arrowsize=1.5pt 2](9,1,00.00)(9,2,00.00)(9,3,00.00)(9,4,00.0)(9,5,00.0)(9,6,00.0)(9,7,00.0)(9,8,00.0)(9,9,00.0)(9,10,00.0)(9,11,00.0)(9,12,00.0)(9,13,00.0)(9,14,00.0)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](1,1,07.60)(1,2,07.60)(1,3,07.60)(1,4,07.80)(1,5,07.80)(1,6,07.80)(1,7,07.80)(1,8,08.10)(1,9,08.10)(1,10,08.10)(1,11,08.10)(1,12,08.30)(1,13,08.30)(1,14,08.30)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](5,1,03.00)(5,2,03.00)(5,3,03.00)(5,4,02.70)(5,5,02.70)(5,6,02.70)(5,7,02.70)(5,8,03.70)(5,9,03.70)(5,10,03.70)(5,11,03.70)(5,12,04.30)(5,13,04.30)(5,14,04.30)
\pstThreeDLine[linewidth=8pt,linecolor=blue,arrowsize=1.5pt 2](9,1,01.40)(9,2,01.40)(9,3,01.40)(9,4,00.50)(9,5,00.50)(9,6,00.50)(9,7,00.50)(9,8,00.50)(9,9,00.50)(9,10,00.50)(9,11,00.50)(9,12,00.50)(9,13,00.50)(9,14,00.50)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](1,1,07.10)(1,2,05.9)(1,3,05.80)(1,4,05.80)(1,5,05.2)(1,6,06.70)(1,7,05.70)(1,8,07.50)(1,9,07.30)(1,10,07.20)(1,11,07.60)(1,12,08.40)(1,13,08.70)(1,14,08.10)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](5,1,01.00)(5,2,01.00)(5,3,01.10)(5,4,01.4)(5,5,01.50)(5,6,01.50)(5,7,01.30)(5,8,02.10)(5,9,01.90)(5,10,01.80)(5,11,02.0)(5,12,02.7)(5,13,02.6)(5,14,02.8)
\pstThreeDLine[linewidth=2pt,linecolor=green,arrowsize=1.5pt 2](9,1,0.00)(9,2,0.100)(9,3,0.000)(9,4,0.00)(9,5,0.00)(9,6,0.00)(9,7,0.00)(9,8,0.00)(9,9,0.00)(9,10,0.00)(9,11,0.00)(9,12,0.00)(9,13,0.00)(9,14,0.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](1,1,06.80)(1,2,06.30)(1,3,06.70)(1,4,07.80)(1,5,06.80)(1,6,07.50)(1,7,07.80)(1,8,08.00)(1,9,08.60)(1,10,08.20)(1,11,08.20)(1,12,08.60)(1,13,08.50)(1,14,08.3)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](5,1,02.40)(5,2,02.6)(5,3,02.50)(5,4,02.40)(5,5,02.5)(5,6,02.60)(5,7,02.60)(5,8,03.60)(5,9,03.3)(5,10,02.80)(5,11,02.90)(5,12,04.2)(5,13,04.20)(5,14,04.20)
\pstThreeDLine[linewidth=2pt,linecolor=red,arrowsize=1.5pt 2](9,1,01.10)(9,2,00.90)(9,3,01.00)(9,4,00.60)(9,5,00.50)(9,6,00.50)(9,7,00.5)(9,8,00.50)(9,9,00.60)(9,10,00.50)(9,11,00.60)(9,12,00.50)(9,13,00.60)(9,14,00.70)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](1,1,10.00)(1,2,10.00)(1,3,10.00)(1,4,10.0)(1,5,10.0)(1,6,10.0)(1,7,10.0)(1,8,10.00)(1,9,10.00)(1,10,10.00)(1,11,10.00)(1,12,10.00)(1,13,10.00)(1,14,10.00)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](5,1,08.50)(5,2,08.50)(5,3,08.50)(5,4,03.70)(5,5,03.70)(5,6,03.70)(5,7,03.70)(5,8,03.3)(5,9,03.3)(5,10,03.3)(5,11,03.3)(5,12,03.3)(5,13,03.3)(5,14,03.3)
\pstThreeDLine[linewidth=8pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](9,1,07.00)(9,2,07.00)(9,3,07.00)(9,4,00.4)(9,5,00.4)(9,6,00.4)(9,7,00.4)(9,8,00.4)(9,9,00.4)(9,10,00.4)(9,11,00.4)(9,12,00.40)(9,13,00.40)(9,14,00.40)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](1,1,06.30)(1,2,06.30)(1,3,06.00)(1,4,06.3)(1,5,06.3)(1,6,07.30)(1,7,07.30)(1,8,07.70)(1,9,08.00)(1,10,08.60)(1,11,07.80)(1,12,07.50)(1,13,07.90)(1,14,08.20)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](5,1,04.10)(5,2,04.20)(5,3,04.30)(5,4,02.00)(5,5,01.60)(5,6,01.80)(5,7,01.80)(5,8,05.0)(5,9,05.0)(5,10,05.0)(5,11,05.0)(5,12,05.0)(5,13,05.0)(5,14,05.0)
\pstThreeDLine[linewidth=8pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](9,1,03.4)(9,2,03.30)(9,3,03.30)(9,4,00.10)(9,5,00.20)(9,6,00.2)(9,7,00.1)(9,8,00.20)(9,9,00.20)(9,10,00.2)(9,11,00.2)(9,12,00.30)(9,13,00.20)(9,14,00.10)
\def\psxyzlabel#1{\bgroup\large\bf\textsf{#1}\egroup}
%
\pstThreeDCoor
[IIIDxTicksPlane=xz,IIIDxticksep=-0.6,IIIDyTicksPlane=yz,IIIDyticksep=-0.2,arrowsize=1.5pt 4,linewidth=1.5pt,linecolor=darkgray,IIIDzTicksPlane=yz,yMin=0,yMax=15.5,xMin=0,xMax=10.5,zMin=0,zMax=11,IIIDticks=true,IIIDticksize=0.0,Dy=025,Dx=0.05,Dz=0.1,IIIDlabels=true,IIIDOffset={(0,0,0)}] 
%
\end{pspicture}
}
%
\end{minipage}
%%
\vspace*{0.0in}
%
\caption{\label{newfig4-full}Effect of variations of the total external to internal asset ratio $\nicefrac{E}{I}$ on the vulnerability index $\xi$ for homogeneous networks.
Lower values of $\xi$ imply higher global stability of a network.}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





















\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% newfig5-coordinated-and-random
%%%\input{../tex-figures/newfig5-coordinated-and-random.tex}

\begin{figure*}
%
\vspace*{0.5in}
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.95}[0.7]{
\begin{pspicture}(1.5,-11.5)(3.5,8)
\psset{xunit=0.010in,yunit=2.5in}
\rput(175,-0.2){(A)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,1.05)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,1.05)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](300,1.55)(335,1.55)
\rput[mr](285,1.55){\bf\footnotesize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](665,1.55)(700,1.55)
\rput[mr](655,1.55){\bf\footnotesize {\sf ER} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](300,1.48)(335,1.48)
\rput[mr](285,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](665,1.48)(700,1.48)
\rput[mr](655,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](300,1.41)(335,1.41)
\rput[mr](285,1.41){\bf\footnotesize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](665,1.41)(700,1.41)
\rput[mr](655,1.41){\bf\footnotesize {\sf SF} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](300,1.34)(335,1.34)
\rput[mr](285,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](665,1.34)(700,1.34)
\rput[mr](655,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](300,1.27)(335,1.27)
\rput[mr](285,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](720,1.27)(755,1.27)
\rput[mr](710,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), idiosyncratic shock}
%
\rput[ml](0.10,1.17){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,1.1){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
%
\rput[mr](-35,0.5){$\pmb{\xi}$}
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.996)(050,0.998)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.942)(050,0.942)(075,0.944)(100,0.944)(125,0.944)(150,0.944)(175,0.944)(200,0.944)(225,0.946)(250,0.946)(275,0.946)(300,0.946)(325,0.946)(350,0.946)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.69)(050,0.60)(075,0.712)(100,0.67)(125,0.726)(150,0.674)(175,0.504)(200,0.808)(225,0.716)(250,0.532)(275,0.658)(300,0.63)(325,0.654)(350,0.672)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.51)(050,0.496)(075,0.518)(100,0.50)(125,0.562)(150,0.616)(175,0.538)(200,0.612)(225,0.546)(250,0.46)(275,0.514)(300,0.638)(325,0.616)(350,0.542)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,1.00)(050,1.00)(075,1.00)(100,1.00)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.868)(050,0.814)(075,0.898)(100,0.898)(125,0.818)(150,0.816)(175,0.816)(200,0.814)(225,0.816)(250,0.88)(275,0.816)(300,0.888)(325,0.816)(350,0.818)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.554)(050,0.442)(075,0.444)(100,0.454)(125,0.458)(150,0.306)(175,0.64)(200,0.29)(225,0.304)(250,0.398)(275,0.646)(300,0.48)(325,0.65)(350,0.414)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.314)(050,0.364)(075,0.28)(100,0.39)(125,0.478)(150,0.332)(175,0.32)(200,0.39)(225,0.406)(250,0.378)(275,0.244)(300,0.412)(325,0.544)(350,0.342)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.942)(050,0.942)(075,0.942)(100,0.942)(125,0.94)(150,0.94)(175,0.94)(200,0.94)(225,0.94)(250,0.94)(275,0.94)(300,0.94)(325,0.94)(350,0.94)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.258)(050,0.284)(075,0.238)(100,0.234)(125,0.204)(150,0.332)(175,0.416)(200,0.326)(225,0.282)(250,0.18)(275,0.252)(300,0.252)(325,0.234)(350,0.19)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%
\hspace*{1.5in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\subfigure{
\scalebox{0.95}[0.7]{
\begin{pspicture}(-2,-11.5)(0,-8.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(B)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,1.05)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,1.05)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,1.17){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,1.1){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.912)(050,0.974)(075,0.98)(100,0.986)(125,0.99)(150,0.992)(175,0.994)(200,0.994)(225,0.996)(250,0.996)(275,0.996)(300,0.996)(325,0.996)(350,0.996)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.874)(050,0.892)(075,0.908)(100,0.91)(125,0.914)(150,0.916)(175,0.916)(200,0.916)(225,0.918)(250,0.918)(275,0.92)(300,0.92)(325,0.92)(350,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.136)(050,0.204)(075,0.464)(100,0.346)(125,0.41)(150,0.508)(175,0.364)(200,0.40)(225,0.386)(250,0.41)(275,0.252)(300,0.402)(325,0.512)(350,0.14)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.174)(050,0.232)(075,0.408)(100,0.204)(125,0.314)(150,0.266)(175,0.258)(200,0.378)(225,0.21)(250,0.276)(275,0.414)(300,0.368)(325,0.22)(350,0.274)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.832)(050,0.982)(075,0.992)(100,0.994)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.708)(050,0.798)(075,0.804)(100,0.836)(125,0.834)(150,0.812)(175,0.812)(200,0.81)(225,0.814)(250,0.85)(275,0.814)(300,0.844)(325,0.844)(350,0.846)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.104)(050,0.236)(075,0.302)(100,0.274)(125,0.378)(150,0.266)(175,0.382)(200,0.274)(225,0.324)(250,0.216)(275,0.412)(300,0.218)(325,0.286)(350,0.216)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.184)(050,0.244)(075,0.166)(100,0.168)(125,0.258)(150,0.232)(175,0.18)(200,0.234)(225,0.176)(250,0.218)(275,0.172)(300,0.228)(325,0.174)(350,0.202)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.868)(050,0.87)(075,0.87)(100,0.87)(125,0.87)(150,0.87)(175,0.87)(200,0.87)(225,0.87)(250,0.87)(275,0.87)(300,0.87)(325,0.87)(350,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.134)(050,0.19)(075,0.14)(100,0.216)(125,0.164)(150,0.114)(175,0.128)(200,0.218)(225,0.22)(250,0.248)(275,0.146)(300,0.15)(325,0.148)(350,0.262)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\vspace*{-4.6in}
\hspace*{3.0in}
%
\subfigure{
\scalebox{0.8}[0.7]{
%%\begin{pspicture}(10.7,-2)(12.7,11.5)
\begin{pspicture}(10.7,-15)(12.7,-1.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(C)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,1.05)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,1.05)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,1.17){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,1.1){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.45}$}
%
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.038)(050,0.238)(075,0.412)(100,0.476)(125,0.522)(150,0.566)(175,0.604)(200,0.636)(225,0.662)(250,0.686)(275,0.718)(300,0.732)(325,0.746)(350,0.748)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.228)(050,0.41)(075,0.506)(100,0.548)(125,0.582)(150,0.60)(175,0.62)(200,0.638)(225,0.648)(250,0.662)(275,0.668)(300,0.676)(325,0.686)(350,0.69)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.034)(050,0.072)(075,0.114)(100,0.122)(125,0.106)(150,0.086)(175,0.126)(200,0.146)(225,0.118)(250,0.122)(275,0.122)(300,0.106)(325,0.142)(350,0.102)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.066)(050,0.102)(075,0.102)(100,0.136)(125,0.146)(150,0.098)(175,0.092)(200,0.168)(225,0.146)(250,0.10)(275,0.142)(300,0.156)(325,0.162)(350,0.152)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.00)(050,0.01)(075,0.034)(100,0.078)(125,0.15)(150,0.21)(175,0.27)(200,0.336)(225,0.39)(250,0.454)(275,0.506)(300,0.53)(325,0.57)(350,0.596)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.006)(050,0.018)(075,0.06)(100,0.12)(125,0.17)(150,0.244)(175,0.318)(200,0.34)(225,0.346)(250,0.37)(275,0.422)(300,0.454)(325,0.438)(350,0.444)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.04)(050,0.034)(075,0.038)(100,0.054)(125,0.05)(150,0.05)(175,0.052)(200,0.044)(225,0.06)(250,0.062)(275,0.062)(300,0.056)(325,0.046)(350,0.06)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.07)(050,0.072)(075,0.074)(100,0.084)(125,0.094)(150,0.092)(175,0.118)(200,0.132)(225,0.114)(250,0.088)(275,0.114)(300,0.098)(325,0.096)(350,0.104)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.264)(050,0.438)(075,0.496)(100,0.516)(125,0.52)(150,0.536)(175,0.55)(200,0.55)(225,0.556)(250,0.556)(275,0.56)(300,0.564)(325,0.568)(350,0.58)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.022)(050,0.106)(075,0.144)(100,0.148)(125,0.114)(150,0.178)(175,0.154)(200,0.122)(225,0.118)(250,0.162)(275,0.134)(300,0.138)(325,0.112)(350,0.136)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hspace*{-0.1in}
%
\subfigure{
\scalebox{0.8}[0.7]{
%%\begin{pspicture}(3,-2)(5,11.5)
\begin{pspicture}(3,-15)(5,-1.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(D)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,1.05)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,1.05)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,1.05)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,1.05)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.5){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,1.17){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,1.1){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.912)(050,0.974)(075,0.98)(100,0.986)(125,0.99)(150,0.992)(175,0.994)(200,0.994)(225,0.996)(250,0.996)(275,0.996)(300,0.996)(325,0.996)(350,0.996)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.874)(050,0.892)(075,0.908)(100,0.91)(125,0.914)(150,0.916)(175,0.916)(200,0.916)(225,0.918)(250,0.918)(275,0.92)(300,0.92)(325,0.92)(350,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.136)(050,0.204)(075,0.464)(100,0.346)(125,0.41)(150,0.508)(175,0.364)(200,0.40)(225,0.386)(250,0.41)(275,0.252)(300,0.402)(325,0.512)(350,0.14)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.174)(050,0.232)(075,0.408)(100,0.204)(125,0.314)(150,0.266)(175,0.258)(200,0.378)(225,0.21)(250,0.276)(275,0.414)(300,0.368)(325,0.22)(350,0.274)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.832)(050,0.982)(075,0.992)(100,0.994)(125,1.00)(150,1.00)(175,1.00)(200,1.00)(225,1.00)(250,1.00)(275,1.00)(300,1.00)(325,1.00)(350,1.00)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.708)(050,0.798)(075,0.804)(100,0.836)(125,0.834)(150,0.812)(175,0.812)(200,0.81)(225,0.814)(250,0.85)(275,0.814)(300,0.844)(325,0.844)(350,0.846)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.104)(050,0.236)(075,0.302)(100,0.274)(125,0.378)(150,0.266)(175,0.382)(200,0.274)(225,0.324)(250,0.216)(275,0.412)(300,0.218)(325,0.286)(350,0.216)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.184)(050,0.244)(075,0.166)(100,0.168)(125,0.258)(150,0.232)(175,0.18)(200,0.234)(225,0.176)(250,0.218)(275,0.172)(300,0.228)(325,0.174)(350,0.202)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.868)(050,0.87)(075,0.87)(100,0.87)(125,0.87)(150,0.87)(175,0.87)(200,0.87)(225,0.87)(250,0.87)(275,0.87)(300,0.87)(325,0.87)(350,0.87)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.134)(050,0.19)(075,0.14)(100,0.216)(125,0.164)(150,0.114)(175,0.128)(200,0.218)(225,0.22)(250,0.238)(275,0.146)(300,0.15)(325,0.148)(350,0.262)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%\vspace*{-0.1in}
\hspace*{-0.0in}
%
\subfigure{
\scalebox{0.95}[0.7]{
%%\begin{pspicture}(1.4,-2)(3.4,11.5)
\begin{pspicture}(1.4,-21)(3.4,-9.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(E)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.5,Dx=25,Dy=0.1](328,0.55)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.55)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.55)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.55)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.25){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](50,0.62){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](50,0.55){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
\psset{origin={-25,-0.5}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.981)(050,0.995)(075,0.995)(100,0.996)(125,0.996)(150,0.994)(175,0.994)(200,0.994)(225,0.993)(250,0.993)(275,0.993)(300,0.992)(325,0.993)(350,0.993)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.887)(050,0.893)(075,0.895)(100,0.894)(125,0.894)(150,0.891)(175,0.89)(200,0.887)(225,0.885)(250,0.88)(275,0.881)(300,0.882)(325,0.881)(350,0.878)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.778)(050,0.879)(075,0.852)(100,0.884)(125,0.887)(150,0.877)(175,0.914)(200,0.905)(225,0.91)(250,0.929)(275,0.91)(300,0.914)(325,0.92)(350,0.90)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.722)(050,0.696)(075,0.768)(100,0.772)(125,0.776)(150,0.762)(175,0.777)(200,0.789)(225,0.711)(250,0.791)(275,0.778)(300,0.765)(325,0.778)(350,0.776)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.972)(050,0.988)(075,0.992)(100,0.995)(125,0.998)(150,0.998)(175,0.998)(200,0.998)(225,0.998)(250,0.998)(275,0.998)(300,0.998)(325,0.998)(350,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.933)(050,0.947)(075,0.947)(100,0.947)(125,0.947)(150,0.947)(175,0.947)(200,0.947)(225,0.947)(250,0.947)(275,0.947)(300,0.947)(325,0.947)(350,0.947)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.714)(050,0.857)(075,0.903)(100,0.83)(125,0.884)(150,0.877)(175,0.895)(200,0.898)(225,0.857)(250,0.928)(275,0.90)(300,0.917)(325,0.911)(350,0.906)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.71)(050,0.741)(075,0.719)(100,0.788)(125,0.762)(150,0.775)(175,0.75)(200,0.765)(225,0.786)(250,0.782)(275,0.763)(300,0.756)(325,0.819)(350,0.759)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.608)(050,0.609)(075,0.609)(100,0.609)(125,0.609)(150,0.609)(175,0.609)(200,0.609)(225,0.609)(250,0.609)(275,0.609)(300,0.609)(325,0.609)(350,0.609)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.646)(050,0.668)(075,0.645)(100,0.621)(125,0.675)(150,0.621)(175,0.681)(200,0.631)(225,0.647)(250,0.634)(275,0.625)(300,0.666)(325,0.637)(350,0.65)
%
\psset{origin={0,0}}
\end{pspicture}
}
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\scalebox{0.95}[0.7]{
\begin{pspicture}(-6.3,-21)(-4.3,-18)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(F)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.70,Dx=25,Dy=0.10](328,0.35)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.35)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.35)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.175){$\pmb{\xi}$}
%
\psset{origin={-25,-0.70}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.47){\footnotesize $\pmb{\alpha=0.10}$ \hspace*{0.1in} $\pmb{\beta=0.95}$}
\rput[ml](0.10,0.40){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.993)(050,0.994)(075,0.995)(100,0.995)(125,0.995)(150,0.997)(175,0.997)(200,0.996)(225,0.996)(250,0.997)(275,0.996)(300,0.996)(325,0.996)(350,0.996)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.937)(050,0.948)(075,0.949)(100,0.955)(125,0.959)(150,0.959)(175,0.959)(200,0.958)(225,0.959)(250,0.959)(275,0.96)(300,0.96)(325,0.96)(350,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.904)(050,0.931)(075,0.948)(100,0.95)(125,0.946)(150,0.959)(175,0.959)(200,0.949)(225,0.967)(250,0.948)(275,0.966)(300,0.96)(325,0.951)(350,0.96)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.877)(050,0.903)(075,0.895)(100,0.911)(125,0.926)(150,0.911)(175,0.896)(200,0.91)(225,0.925)(250,0.91)(275,0.91)(300,0.922)(325,0.929)(350,0.916)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.998)(050,0.998)(075,0.998)(100,0.998)(125,0.998)(150,0.998)(175,0.998)(200,0.998)(225,0.998)(250,0.998)(275,0.998)(300,0.998)(325,0.998)(350,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.948)(050,0.948)(075,0.948)(100,0.948)(125,0.948)(150,0.948)(175,0.948)(200,0.948)(225,0.948)(250,0.948)(275,0.948)(300,0.948)(325,0.948)(350,0.948)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.975)(050,0.98)(075,0.979)(100,0.984)(125,0.99)(150,0.976)(175,0.988)(200,0.986)(225,0.987)(250,0.97)(275,0.984)(300,0.98)(325,0.979)(350,0.984)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.919)(050,0.917)(075,0.905)(100,0.934)(125,0.932)(150,0.931)(175,0.942)(200,0.915)(225,0.904)(250,0.921)(275,0.915)(300,0.925)(325,0.897)(350,0.923)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.986)(050,0.979)(075,0.979)(100,0.97)(125,0.97)(150,0.97)(175,0.97)(200,0.97)(225,0.97)(250,0.97)(275,0.97)(300,0.97)(325,0.97)(350,0.97)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.819)(050,0.818)(075,0.826)(100,0.827)(125,0.802)(150,0.859)(175,0.801)(200,0.822)(225,0.809)(250,0.812)(275,0.824)(300,0.844)(325,0.787)(350,0.848)
%
\psset{origin={0,0}}
%
\end{pspicture}
}

\vspace*{-5.3in}
\caption{\label{newfig5-full}Effect of variations of the total external to internal asset ratio $\nicefrac{E}{I}$ on the vulnerability index $\xi$
for $(\alpha,\beta)$-heterogeneous networks. Lower values of $\xi$ imply higher global stability of a network.}
%
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%























\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% supp-newfig5-coordinated-and-random
%%%\input{../tex-figures/supp-newfig5-coordinated-and-random.tex}

\begin{figure*}
%
\vspace*{0.7in}
%%%\hspace*{0.2in}
%
\subfigure{
\scalebox{1}[0.8]{
\begin{pspicture}(1.5,-6.5)(3.5,8)
\psset{xunit=0.010in,yunit=2.5in}
\rput(175,-0.2){(A)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.1,Dx=25,Dy=0.1](328,0.95)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.95)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.95)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.95)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](300,1.55)(335,1.55)
\rput[mr](285,1.55){\bf\footnotesize {\sf ER} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](665,1.55)(700,1.55)
\rput[mr](655,1.55){\bf\footnotesize {\sf ER} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](300,1.48)(335,1.48)
\rput[mr](285,1.48){\bf\footnotesize {\sf ER} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](665,1.48)(700,1.48)
\rput[mr](655,1.48){\bf\footnotesize {\sf ER} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](300,1.41)(335,1.41)
\rput[mr](285,1.41){\bf\footnotesize {\sf SF} model (average degree $6$), coordinated shock}
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](665,1.41)(700,1.41)
\rput[mr](655,1.41){\bf\footnotesize {\sf SF} model (average degree $3$), coordinated shock}
%%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](300,1.34)(335,1.34)
\rput[mr](285,1.34){\bf\footnotesize {\sf SF} model (average degree $6$), idiosyncratic shock}
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](665,1.34)(700,1.34)
\rput[mr](655,1.34){\bf\footnotesize {\sf SF} model (average degree $3$), idiosyncratic shock}
%%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](310,1.27)(345,1.27)
\rput[mr](295,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), coordinated shock}
%%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](730,1.27)(765,1.27)
\rput[mr](720,1.27){\bf\footnotesize in-arborescence (average degree $\approx 1$), idiosyncratic shock}
%
\rput[ml](0.10,1.07){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,1.0){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.45){$\pmb{\xi}$}
%
\psset{origin={-25,-0.1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.962)(050,0.978)(075,0.98)(100,0.98)(125,0.982)(150,0.982)(175,0.984)(200,0.984)(225,0.984)(250,0.984)(275,0.984)(300,0.984)(325,0.986)(350,0.986)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.872)(050,0.89)(075,0.892)(100,0.896)(125,0.898)(150,0.902)(175,0.902)(200,0.902)(225,0.902)(250,0.902)(275,0.902)(300,0.902)(325,0.902)(350,0.902)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.62)(050,0.53)(075,0.69)(100,0.606)(125,0.666)(150,0.704)(175,0.70)(200,0.674)(225,0.52)(250,0.694)(275,0.654)(300,0.638)(325,0.646)(350,0.664)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.484)(050,0.584)(075,0.556)(100,0.514)(125,0.686)(150,0.582)(175,0.492)(200,0.568)(225,0.564)(250,0.62)(275,0.54)(300,0.624)(325,0.554)(350,0.60)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.972)(050,0.978)(075,0.978)(100,0.978)(125,0.978)(150,0.978)(175,0.978)(200,0.978)(225,0.978)(250,0.978)(275,0.978)(300,0.978)(325,0.978)(350,0.978)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.804)(050,0.806)(075,0.812)(100,0.814)(125,0.814)(150,0.814)(175,0.814)(200,0.814)(225,0.814)(250,0.814)(275,0.814)(300,0.818)(325,0.818)(350,0.818)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.474)(050,0.304)(075,0.634)(100,0.43)(125,0.504)(150,0.552)(175,0.422)(200,0.518)(225,0.578)(250,0.48)(275,0.458)(300,0.432)(325,0.426)(350,0.424)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.294)(050,0.354)(075,0.392)(100,0.332)(125,0.434)(150,0.46)(175,0.368)(200,0.352)(225,0.368)(250,0.41)(275,0.322)(300,0.398)(325,0.47)(350,0.372)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.798)(050,0.786)(075,0.784)(100,0.784)(125,0.784)(150,0.782)(175,0.782)(200,0.782)(225,0.782)(250,0.782)(275,0.782)(300,0.782)(325,0.782)(350,0.782)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.228)(050,0.176)(075,0.284)(100,0.16)(125,0.278)(150,0.152)(175,0.232)(200,0.226)(225,0.254)(250,0.246)(275,0.228)(300,0.154)(325,0.23)(350,0.18)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%%%%%%%%%%%%
\hspace*{1.5in}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 2 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\subfigure{
\scalebox{1}[0.8]{
\begin{pspicture}(-2,-6.5)(0,8)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(B)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,0.45)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.45)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.45)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.225){$\pmb{\xi}$}
%
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.57){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.5){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.182)(050,0.242)(075,0.268)(100,0.298)(125,0.298)(150,0.304)(175,0.31)(200,0.316)(225,0.32)(250,0.32)(275,0.328)(300,0.33)(325,0.332)(350,0.332)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.30)(050,0.336)(075,0.35)(100,0.35)(125,0.354)(150,0.354)(175,0.356)(200,0.356)(225,0.358)(250,0.36)(275,0.36)(300,0.36)(325,0.36)(350,0.36)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.08)(050,0.132)(075,0.14)(100,0.124)(125,0.14)(150,0.114)(175,0.128)(200,0.144)(225,0.134)(250,0.144)(275,0.132)(300,0.142)(325,0.15)(350,0.122)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.136)(050,0.206)(075,0.25)(100,0.134)(125,0.164)(150,0.154)(175,0.12)(200,0.138)(225,0.16)(250,0.152)(275,0.178)(300,0.22)(325,0.154)(350,0.152)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.10)(100,0.106)(125,0.11)(150,0.114)(175,0.116)(200,0.116)(225,0.12)(250,0.12)(275,0.122)(300,0.122)(325,0.124)(350,0.124)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.112)(050,0.138)(075,0.148)(100,0.148)(125,0.152)(150,0.158)(175,0.162)(200,0.164)(225,0.168)(250,0.17)(275,0.17)(300,0.172)(325,0.172)(350,0.172)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.104)(050,0.106)(075,0.11)(100,0.104)(125,0.104)(150,0.102)(175,0.102)(200,0.104)(225,0.102)(250,0.108)(275,0.11)(300,0.106)(325,0.104)(350,0.113)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.106)(050,0.104)(075,0.108)(100,0.104)(125,0.108)(150,0.10)(175,0.116)(200,0.104)(225,0.112)(250,0.106)(275,0.122)(300,0.104)(325,0.106)(350,0.104)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.26)(050,0.262)(075,0.262)(100,0.262)(125,0.262)(150,0.262)(175,0.262)(200,0.262)(225,0.262)(250,0.262)(275,0.262)(300,0.262)(325,0.262)(350,0.262)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.114)(050,0.13)(075,0.122)(100,0.126)(125,0.11)(150,0.14)(175,0.136)(200,0.138)(225,0.122)(250,0.116)(275,0.142)(300,0.138)(325,0.124)(350,0.154)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 3 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\hspace*{0.1in}
%
\subfigure{
\scalebox{1}[0.8]{
\begin{pspicture}(1.5,-16)(3.5,-2.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(C)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,0.15)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.15)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.15)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.15)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.05){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.27){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.2){\footnotesize $\pmb{|V|=50}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.45}$}
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.024)(050,0.088)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.072)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.012)(050,0.042)(075,0.054)(100,0.062)(125,0.076)(150,0.062)(175,0.076)(200,0.068)(225,0.09)(250,0.084)(275,0.096)(300,0.092)(325,0.096)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.046)(050,0.07)(075,0.066)(100,0.082)(125,0.096)(150,0.094)(175,0.094)(200,0.098)(225,0.098)(250,0.098)(275,0.10)(300,0.098)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.00)(050,0.006)(075,0.03)(100,0.076)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.004)(050,0.02)(075,0.03)(100,0.062)(125,0.086)(150,0.092)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.018)(050,0.034)(075,0.072)(100,0.098)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.044)(050,0.076)(075,0.078)(100,0.09)(125,0.10)(150,0.098)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.10)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.066)(050,0.10)(075,0.10)(100,0.10)(125,0.10)(150,0.10)(175,0.10)(200,0.10)(225,0.10)(250,0.10)(275,0.10)(300,0.10)(325,0.10)(350,0.10)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 4 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\subfigure{
\scalebox{1}[0.8]{
\begin{pspicture}(-6.25,-14)(-4.25,-0.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(D)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0,Dx=25,Dy=0.1](328,0.45)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.45)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.45)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.45)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-35,0.2){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.57){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.5){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.1}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
%
\psset{origin={-25,0}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.271)(050,0.306)(075,0.319)(100,0.331)(125,0.337)(150,0.344)(175,0.348)(200,0.35)(225,0.351)(250,0.351)(275,0.351)(300,0.351)(325,0.352)(350,0.352)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.361)(050,0.374)(075,0.383)(100,0.384)(125,0.384)(150,0.384)(175,0.385)(200,0.386)(225,0.386)(250,0.386)(275,0.386)(300,0.386)(325,0.386)(350,0.386)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.109)(050,0.141)(075,0.124)(100,0.137)(125,0.136)(150,0.15)(175,0.139)(200,0.134)(225,0.138)(250,0.128)(275,0.121)(300,0.127)(325,0.15)(350,0.144)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.148)(050,0.219)(075,0.134)(100,0.143)(125,0.218)(150,0.222)(175,0.143)(200,0.147)(225,0.155)(250,0.234)(275,0.131)(300,0.23)(325,0.143)(350,0.225)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.121)(050,0.136)(075,0.14)(100,0.143)(125,0.148)(150,0.148)(175,0.148)(200,0.149)(225,0.15)(250,0.151)(275,0.151)(300,0.151)(325,0.151)(350,0.152)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.137)(050,0.142)(075,0.148)(100,0.149)(125,0.152)(150,0.156)(175,0.156)(200,0.156)(225,0.156)(250,0.156)(275,0.156)(300,0.156)(325,0.156)(350,0.156)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.101)(050,0.104)(075,0.104)(100,0.106)(125,0.103)(150,0.101)(175,0.104)(200,0.105)(225,0.103)(250,0.105)(275,0.103)(300,0.106)(325,0.102)(350,0.104)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.102)(050,0.102)(075,0.106)(100,0.107)(125,0.106)(150,0.108)(175,0.103)(200,0.107)(225,0.11)(250,0.112)(275,0.103)(300,0.109)(325,0.11)(350,0.103)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.244)(050,0.244)(075,0.244)(100,0.244)(125,0.244)(150,0.244)(175,0.244)(200,0.244)(225,0.244)(250,0.244)(275,0.244)(300,0.244)(325,0.244)(350,0.244)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.122)(050,0.125)(075,0.114)(100,0.117)(125,0.115)(150,0.11)(175,0.119)(200,0.115)(225,0.126)(250,0.124)(275,0.122)(300,0.127)(325,0.119)(350,0.12)
%
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%
\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 5 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\hspace*{0.1in}
%
\subfigure{
\scalebox{1}[0.8]{
\begin{pspicture}(1.5,-16.5)(3.5,-9.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(E)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.4,Dx=25,Dy=0.1](328,0.65)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.65)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.65)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.65)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-40,0.275){$\pmb{\xi}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](50,0.72){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](50,0.65){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.25}$}
%
\psset{origin={-25,-0.4}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.842)(050,0.846)(075,0.893)(100,0.898)(125,0.901)(150,0.902)(175,0.904)(200,0.905)(225,0.905)(250,0.906)(275,0.906)(300,0.907)(325,0.908)(350,0.908)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.793)(050,0.802)(075,0.803)(100,0.805)(125,0.805)(150,0.805)(175,0.805)(200,0.805)(225,0.805)(250,0.805)(275,0.806)(300,0.806)(325,0.806)(350,0.806)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.617)(050,0.657)(075,0.686)(100,0.683)(125,0.673)(150,0.679)(175,0.689)(200,0.693)(225,0.708)(250,0.676)(275,0.681)(300,0.674)(325,0.681)(350,0.699)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.632)(050,0.691)(075,0.669)(100,0.679)(125,0.615)(150,0.657)(175,0.701)(200,0.621)(225,0.693)(250,0.653)(275,0.662)(300,0.66)(325,0.686)(350,0.686)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.521)(050,0.535)(075,0.539)(100,0.542)(125,0.546)(150,0.546)(175,0.546)(200,0.547)(225,0.548)(250,0.549)(275,0.549)(300,0.549)(325,0.549)(350,0.549)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.536)(050,0.538)(075,0.542)(100,0.543)(125,0.545)(150,0.547)(175,0.547)(200,0.547)(225,0.547)(250,0.547)(275,0.547)(300,0.547)(325,0.547)(350,0.547)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.527)(050,0.543)(075,0.537)(100,0.544)(125,0.544)(150,0.543)(175,0.535)(200,0.545)(225,0.534)(250,0.547)(275,0.553)(300,0.546)(325,0.549)(350,0.557)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.53)(050,0.534)(075,0.549)(100,0.556)(125,0.537)(150,0.551)(175,0.53)(200,0.553)(225,0.562)(250,0.544)(275,0.551)(300,0.536)(325,0.548)(350,0.548)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.494)(050,0.494)(075,0.494)(100,0.494)(125,0.494)(150,0.494)(175,0.494)(200,0.494)(225,0.494)(250,0.494)(275,0.494)(300,0.494)(325,0.494)(350,0.494)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.556)(050,0.56)(075,0.542)(100,0.567)(125,0.551)(150,0.556)(175,0.541)(200,0.548)(225,0.547)(250,0.555)(275,0.552)(300,0.555)(325,0.543)(350,0.551)
%
\psset{origin={0,0}}
\end{pspicture}
}
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% part 6 of figure starts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\subfigure{
\scalebox{1}[0.8]{
\begin{pspicture}(-6.25,-15.5)(-4.25,-8.5)
\psset{xunit=0.01in,yunit=2.5in}
\rput(175,-0.2){(F)}
%
\def\pshlabel#1{\scalebox{0.75}{\footnotesize\bf #1\%}}
\def\psvlabel#1{\small\bf #1}
\psaxes[linewidth=1.5pt,Ox=25,Oy=0.70,Dx=25,Dy=0.10](328,0.35)
%
%%%%%%% grid follows
%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.10)(328,0.10)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.20)(328,0.20)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.30)(328,0.30)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.40)(328,0.40)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.50)(328,0.50)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.60)(328,0.60)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.70)(328,0.70)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.80)(328,0.80)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,0.90)(328,0.90)
%%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](0,1.00)(328,1.00)
%%
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](25,0)(25,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](50,0)(50,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](75,0)(75,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](100,0)(100,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](125,0)(125,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](150,0)(150,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](175,0)(175,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](200,0)(200,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](225,0)(225,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](250,0)(250,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](275,0)(275,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](300,0)(300,0.35)
\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](325,0)(325,0.35)
%\psline[linewidth=0.5pt,linecolor=gray,arrowsize=1.5pt 2](350,0)(350,0.35)
%
\rput[mr](-15,-0.065){$\pmb{E}$}
\rput[ml](-30,-0.15){\bf (as \% of $\pmb{I}$)}
%
\rput[mr](-45,0.2){$\pmb{\xi}$}
%
\psset{origin={-25,-0.70}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% legends
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\rput[ml](0.10,0.47){\footnotesize $\pmb{\alpha=0.20}$ \hspace*{0.1in} $\pmb{\beta=0.60}$}
\rput[ml](0.10,0.40){\footnotesize $\pmb{|V|=100}$ \hspace*{0.1in} $\pmb{\mathcal{K}=0.5}$ \hspace*{0.1in}$\pmb{\Phi=0.5}$ \hspace*{0.1in}$\pmb{\gamma=0.05}$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,arrowsize=1.5pt 2](025,0.998)(050,0.998)(075,0.998)(100,0.998)(125,0.998)(150,0.998)(175,0.998)(200,0.998)(225,0.998)(250,0.998)(275,0.998)(300,0.998)(325,0.998)(350,0.998)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=red,arrowsize=1.5pt 2](025,0.957)(050,0.957)(075,0.958)(100,0.958)(125,0.958)(150,0.958)(175,0.958)(200,0.958)(225,0.958)(250,0.958)(275,0.958)(300,0.958)(325,0.958)(350,0.958)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=black,arrowsize=1.5pt 2](025,0.973)(050,0.982)(075,0.978)(100,0.986)(125,0.983)(150,0.979)(175,0.986)(200,0.979)(225,0.977)(250,0.977)(275,0.991)(300,0.987)(325,0.977)(350,0.984)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  ER, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=gray,arrowsize=1.5pt 2](025,0.946)(050,0.926)(075,0.916)(100,0.922)(125,0.907)(150,0.93)(175,0.929)(200,0.933)(225,0.931)(250,0.926)(275,0.926)(300,0.915)(325,0.924)(350,0.92)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=yellow,arrowsize=1.5pt 2](025,0.975)(050,0.975)(075,0.976)(100,0.976)(125,0.976)(150,0.977)(175,0.977)(200,0.978)(225,0.978)(250,0.978)(275,0.978)(300,0.978)(325,0.978)(350,0.978)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, coordinated, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=blue,arrowsize=1.5pt 2](025,0.938)(050,0.938)(075,0.938)(100,0.938)(125,0.938)(150,0.938)(175,0.938)(200,0.938)(225,0.938)(250,0.938)(275,0.938)(300,0.938)(325,0.938)(350,0.938)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=green,arrowsize=1.5pt 2](025,0.933)(050,0.942)(075,0.947)(100,0.952)(125,0.955)(150,0.939)(175,0.961)(200,0.941)(225,0.945)(250,0.939)(275,0.948)(300,0.948)(325,0.935)(350,0.948)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  SF, random, ave degree 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=1pt,linecolor=red,arrowsize=1.5pt 2](025,0.894)(050,0.889)(075,0.902)(100,0.903)(125,0.892)(150,0.894)(175,0.894)(200,0.915)(225,0.908)(250,0.898)(275,0.887)(300,0.898)(325,0.895)(350,0.891)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, coordinated
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=black,linestyle=dashed,arrowsize=1.5pt 2](025,0.971)(050,0.971)(075,0.971)(100,0.971)(125,0.971)(150,0.971)(175,0.971)(200,0.971)(225,0.971)(250,0.971)(275,0.971)(300,0.971)(325,0.971)(350,0.971)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  tree, random
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\psline[linewidth=4pt,linecolor=gray,linestyle=dashed,arrowsize=1.5pt 2](025,0.766)(050,0.783)(075,0.789)(100,0.773)(125,0.761)(150,0.775)(175,0.723)(200,0.771)(225,0.767)(250,0.765)(275,0.807)(300,0.735)(325,0.752)(350,0.795)
%
\psset{origin={0,0}}
%
\end{pspicture}
}
}
%
\vspace*{-4.4in}
\caption{\label{supp-newfig5-full}Effect of variations of the total external to internal asset ratio $\frac{\E}{\I}$ on the vulnerability index $\xi$
for $(\alpha,\beta)$-heterogeneous networks. Lower values of $\xi$ imply higher global stability of a network.}
%
\end{figure*}
%%%%%%%%%%%%%%%%%


\end{document}

1208.3789.extracted_bib
\begin{thebibliography}{99}
\bibitem{Ace2013}
{\sc Acemoglu D., Ozdaglar A. \& Tahbaz-Salehi A.} (2013). Systemic risk and stability in financial networks. working paper.

\bibitem{AG08}
{\sc Allen F. \& Babus A.} (2009). Networks in Finance, 
in: Network-based Strategies and Competencies, Kleindorfer P., Wind J. (Eds.), Wharton School Publishing, 367-382.

\bibitem{AG2000}
{\sc Allen F. \& Gale D.} (2000). Financial Contagion. {\em Journal of Political Economy}, \textbf{108} (1), 1--33.

\bibitem{AS90}
{\sc Alon N. \& Spencer J. H.} (1992). The Probabilistic Method. John Wiley \& Sons, Inc. 

\bibitem{ACM11}
{\sc Amini H., Cont R. \& Minca A.} (2011). Resilience to contagion in financial networks, arXiv:1112.5687v1.

\bibitem{B07}
{\sc Babus A.} (2007a).
The Formation of Financial Networks,
Tinbergen Institute Discussion Paper No. 2006-093/2; FEEM Working Paper No. 69.2007.

\bibitem{A05}
{\sc Babus A.} (2007b). Contagion Risk in Financial Networks, in: Financial Development, Integration and Stability, 
Liebscher K., Christl J., Mooslechner P., Ritzberger-Grunwald D. (Eds.), Edward Elgar Pub, 423--440.

\bibitem{BaAl99}
{\sc Bar\'{a}basi A.-L. \& Albert R.} (1999). Emergence of Scaling in Random Networks. {\em Science}, \textbf{286}, 509--512.

\bibitem{arxiv}
{\sc Berman P., DasGupta B., Kaligounder L. \& Karpinski M.} (2013). On Systemic Stability of Banking Networks, {\em Algorithmica}, in press.

\bibitem{bolo}
{\sc Bollob\'{a}s B.} (2001). Random Graphs. Cambridge University Press.

\bibitem{Bo03}
{\sc Bollob\'{a}s B., Borgs C., Chayes T. \& Riordan O.} (2003). Directed scale-free graphs, 
in: $14\tx$ ACM-SIAM Symposium on Discrete Algorithms, 
Society for Industrial and Applied Mathematics, Philadelphia, PA, 
132-139.

\bibitem{BE98}
{\sc Borodin A. \& El-Yaniv R.} (1998). Online Computation and Competitive Analysis, Cambridge University Press.

\bibitem{borodin}
{\sc Borodin A., Filmus Y. \& Oren J.} (2010).
Threshold models for competitive influence in social networks,
$6\tx$ international conference on Internet and network economics, 
Springer-Verlag Berlin, Heidelberg,  
539--550.

\bibitem{C09}
{\sc Calabria M. A.} (2009). Did Deregulation Cause the Financial Crisis?, Cato Institute.

\bibitem{CNSW00}
{\sc Callaway D. S., Newman M. E. J., Strogatz S. H. \& Watts D. J.} (2000). Network robustness and fragility: percolation on random graphs.
{\em Physical Review Letters}, \textbf{85}, 5468--5471.

\bibitem{FN09}
{\sc Castiglionesi F. \& Navarro B.} (2007).
Optimal Fragile Financial Networks.
Tilburg University Discussion Paper no. 2007-100 (Tilburg, The Netherlands: Tilburg University).

\bibitem{Chen08}
{\sc Chen N.} (2008). On the approximability of influence in social networks, in:  
$19\tx$ ACM-SIAM Symposium on Discrete Algorithms, 
Society for Industrial and Applied Mathematics, Philadelphia, PA, 
1029--1037.

\bibitem{CWY09}
{\sc Chen W., Wang Y. \& Yang S.} (2009). Efficient influence maximization in social networks, in: 
$15\tx$ ACM SIGKDD international conference on Knowledge discovery and data mining, 
Association for Computing Machinery, New York, 
199--208.

\bibitem{coelho08}
{\sc Coelho F. C., Cruz O. G. \& Code�o C. T.} (2008).
Epigrass: a tool to study disease spread in complex networks.
{\em Source Code for Biology and Medicine}, \textbf{3} (3), 2008.

\bibitem{C10}
{\sc Cont R.} (2010). Credit default swaps and financial stability. {\em Finacial Stability Review (Banque de France)}, \textbf{14}, 35--43.

\bibitem{CMS10}
{\sc Cont R., Moussa A. \& Santos E. B.} (2010). Network Structure and Systemic Risk in Banking Systems. Working paper.

\bibitem{CD09}
{\sc Corbo J. \& Demange G.} (2010). in: $3^{\mathrm{rd}}$ Financial Risks International Forum, Paris, France.

\bibitem{D04}
{\sc Dasgupta B.} (2004).
Capital Accumulation in the Presence of Informal Credit Contracts: Does the Incentive Mechanism Work Better than Credit Rationing Under Asymmetric Information?,
Working papers 2004-32, University of Connecticut, Department of Economics.

\bibitem{DP83}
{\sc Diamond D. W. \& Dybvig P. H.} (1983). Bank runs, deposit insurance and liquidity. {\em Journal of Political Economy}, \textbf{91}, 401--419.

\bibitem{E04}
{\sc Eboli M.} (2004). Systemic Risk in Financial Network: a Graph Theoretical Approach. 
Mimeo, Univ. di Chieti, Pescara.

\bibitem{E2013}
{\sc Elliott M., Golub B. \& Jackson M. O.} (2013). Financial networks and contagion. Working paper.

\bibitem{ET08}
{\sc Ekelund R. \& Thornton M.} (2008). More Awful Truths About Republicans. Ludwig von Mises Institute. 

\bibitem{eubank05}
{\sc Eubank S.} (2005).  
Network based models of infectious disease spread.
{\em Japanese Journal of Infectious Diseases}, \textbf{58}, S19-S13.

\bibitem{eubank04}
{\sc Eubank S., Guclu H., Kumar V. S. A., Marathe M. V., Srinivasan A., Toroczkai Z. \& Wang N.} (2004).
Modeling Disease Outbreaks in Realistic Urban Social Networks.
{\em Nature}, \textbf{429}, 180--183.

\bibitem{F33}
{\sc Fisher I.} (1933). The Debt-Deflation Theory of Great Depressions. {\em Econometrica}, \textbf{1}, 337--357.

\bibitem{XBJ2000}
{\sc Freixas X., Parigi B. M. \& Rochet J.-C.} (2000). Systemic risk, interbank relations, and liquidity provision by the central bank.
{\em Journal of Money, Credit and Banking}, \textbf{32} (3), 611--638.

\bibitem{F03}
{\sc Furfine C. H.} (2003). Interbank exposures: Quantifying the risk of contagion. {\em Journal of Money, Credit and Banking}, \textbf{35} (1), 111--128.

\bibitem{GK08}
{\sc Gai P. \& Kapadia S.} (2010). Contagion in financial networks. {\em Proc. R. Soc. A}, \textbf{466} (2120), 2401--2423.

\bibitem{H09}
{\sc Haldane A.} (2009). Why Banks Failed the Stress Test.
speech given at the Marcus-Evans Conference on Stress-Testing, 9-10 February 2009 (available at \url{http://www.bankofengland.co.uk/publications/speeches/2009/speech374.pdf}).

\bibitem{HM11}
{\sc Haldane A. G. \& May R. M.} (2011). Systemic risk in banking ecosystems. {\em Nature}, \textbf{469}, 351--355.

\bibitem{HK00}
{\sc Hann J. \& Kamber M.} (2000). Data Mining: Concepts and Techniques. Morgan Kaufman Publishers.

\bibitem{AW12}
{\sc H\"{u}bsch A. \& Walther U.} (2012). The impact of network inhomogeneities on contagion and system stability, CPQF Working Paper 
Series, No. 32, Frankfurt School of Finance \& Management.

\bibitem{CM09}
{\sc Iazzetta C. \& Manna M.} (2009).
The Topology of the Interbank Market Developements in Italy Since 1990,
Bank of Italy Temi di Discussione (Working Paper) No. 711.

\bibitem{IP06}
{\sc Iyer R. \& Peydro J. L.} (2010). Interbank Contagion at Work: Evidence from a Natural Experiment. {\em Review of Financial Studies}, \textbf{24} (4), 1337--1377.

\bibitem{jones}
{\sc Jones C. M. \& Zhigljavsky A. A.} (2004). Approximating the negative moments of the Poisson distribution.
{\em Statistics \& Probability Letters}, \textbf{66} (2), 171--181.

\bibitem{kempe1}
{\sc Kempe D., Kleinberg J. \& Tardos E.} (2003).
Maximizing the spread of influence through a social network,
$9\tx$ ACM SIGKDD international conference on Knowledge discovery and data mining, 
Association for Computing Machinery, New York, 
137--146.

\bibitem{K36}
{\sc Keynes J. M.} (1936). The General Theory of Employment, Interest, and Money. New York: Harcourt, Brace and Company.

\bibitem{PYR09}
{\sc Kleindorfer P. R., Wind Y. \& Gunther R. E.} (2009). The Network Challenge: Strategy, Profit and Risk in an Interlinked World. Pearson Prentice Hall.

\bibitem{Knuth}
{\sc Knuth D. E.} (1997). The Art of Computer Programming (Fundamental Algorithms), Volume 1, Third Edition, Reading, Massachusetts: Addison-Wesley.

\bibitem{La13}
{\sc Ladley D.} (2013). Contagion and risk sharing on the inter-bank market, {\em Journal of Economics Dynamics \& Control}, \textbf{37}, 1384--1400.

\bibitem{RS98}
{\sc Lagunoff R. \& Schreft S.} (2001). A Model of Financial Fragility. {\em Journal of Economic Theory}, \textbf{99} (1-2), 220--264.

\bibitem{Lie2010}
{\sc Liedorp F. R., Medema L., Koetter M., Koning R. H. \& Lelyveld I. van} (2010).
Peer monitoring or contagion? Interbank market exposure and bank risk,
DNB working paper No. 248.

\bibitem{MGS09}
{\sc Markose S., Giansante S., Gatkowski M. \& Shaghaghi A. R.} (2009).
Too Interconnected To Fail: Financial Contagion and Systemic Risk In Network Model of CDS and Other Credit Enhancement Obligations of 
US Banks. Economics Discussion Papers 683, Department of Economics, University of Essex.

\bibitem{MA10}
{\sc May R. \& Arinaminpathy N.} (2010). Systemic risk: the dynamics of model banking systems. {\em J. R. Soc. Interface}, \textbf{7}, 823--838.

\bibitem{MMM11}
{\sc Minca A.} (2011). Mathematical modeling of default contagion. PhD thesis, Universite Paris VI (Pierre et Marie Curie).

\bibitem{MR13}
{\sc Minoiu C. \& Reyes J. A.} (2013). A Network Analysis of Global Banking: 1978-2010. {\em Journal of Financial Stability} (in press).

\bibitem{M77}
{\sc Minsky H.} (1977). A Theory of Systemic Fragility, in: Financial Crises: Institutions and Markets in a Fragile Environment, Altman E. I., Sametz A. W. (Eds.), Wiley.

\bibitem{M07}
{\sc Mistrulli P. E.} (2007). Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns. Bank of Italy Research.

\bibitem{M11}
{\sc Moussa A.} (2011). Thesis, Columbia University.

\bibitem{NYYA07}
{\sc Nier E., Yang J., Yorulmazer T. \& Alentorn A.} (2007). Network models and financial stability. {\em Journal of Economics Dynamics and Control}, \textbf{31}, 2033--2060.

\bibitem{OKK04}
{\sc Onnela K.-P., Kaski K. \& Kert\'{e}sz J.} (2004). Clustering and information in correlation based financial networks. {\em Eur. Phys. J. B}, \textbf{38}, 353--362.

\bibitem{rozanov}
{\sc Rozanov Y. A.} (1977). Probability Theory: A Concise Course. Dover Publications, Inc. 

\bibitem{A10}
{\sc Sachs A.} (2013). Completeness interconnectedness and distribution of interbank exposures - a parameterized analysis of the stability of financial networks.
{\em Quantitative Finance} (in press).

\bibitem{SR10}
{\sc Santos E. B. \& Cont R.} (2010). The Brazilian Interbank Network Structure and Systemic Risk. Working Papers Series 219, Central Bank of Brazil.

\bibitem{SOKK}
{\sc Saram\"{a}ki J., Onnela J.-P., Kert\'{e}sz J. \& Kaski K.} (2005).
Characterizing Motifs in Weighted Complex Networks, in: Science of Complex Networks, Mendes J. F. F. \EA (Eds.).

\bibitem{SA94}
{\sc Stauffer D. \& Aharony A.} (1994). Introduction to Percolation Theory, 2nd edition, CRC Press.

\bibitem{SM12}
{\sc Staum J. C. \& Liu M.} (2012). Systemic Risk Components in a Network Model of Contagion. Working paper,
Department of Industrial Engineering and Management Sciences, Northwestern University.

\bibitem{UW04}
{\sc Upper C. \& Worms A.} (2004). Estimating bilateral exposures in the german interbank market: Is there a danger of contagion?. {\em European Economic Review}, \textbf{48} (4), 827--849.

\bibitem{Z11}
{\sc Zawadowski A.} (2011). Entangled Financial Systems. Working paper, Boston University School of Management.
\end{thebibliography}