  The approach of quantifying the damage inflicted on a graph in Albert, Jeong
and Barabsi's (AJB) report "Error and Attack Tolerance of Complex Networks"
using the size of the largest connected component and the average size of the
remaining components does not capture our intuitive idea of the damage to a
graph caused by disconnections. We evaluate an alternative metric based on
average inverse path lengths (AIPLs) that better fits our intuition that a
graph can still be reasonably functional even when it is disconnected. We
compare our metric with AJB's using a test set of graphs and report the
differences. AJB's report should not be confused with a report by Crucitti et
al. with the same name. Based on our analysis of graphs of different sizes and
types, and using various numerical and statistical tools; the ratio of the
average inverse path lengths of a connected graph of the same size as the sum
of the size of the fragments of the disconnected graph can be used as a metric
about the damage of a graph by the removal of an edge or a node. This damage is
reported in the range (0,1) where 0 means that the removal had no effect on the
graph's capability to perform its functions. A 1 means that the graph is
totally dysfunctional. We exercise our metric on a collection of sample graphs
that have been subjected to various attack profiles that focus on edge, node or
degree betweenness values. We believe that this metric can be used to quantify
the damage done to the graph by an attacker, and that it can be used in
evaluating the positive effect of adding additional edges to an existing graph.
