  Traditionally, there is no evidence suggesting that there are strong ties
between the rich-club property and the function of complex networks. In this
study, we find that whether a very small portion of rich nodes connected to
each other or not can strongly affect the frequency of occurrence of basic
building blocks (motif) within networks, and therefore the function, of a
heterogeneous network. Conversely whether a homogeneous network has a rich-club
property or not generally has no significant effect on its structure and
function. These findings open the possibility to optimize and control the
function of complex networks by manipulating rich-club connections.
Furthermore, based on the subgraph ratio profile, we develop a more rigorous
approach to judge whether a network has a rich-club or not. The new method does
not calculate how many links there are among rich nodes but depends on how the
links among rich nodes can affect the overall structure as well as function of
a given network. These results can also help us to understand the evolution of
dynamical networks and design new models for characterizing real-world
networks.
