Changing motif distributions in complex networks by manipulating rich-club connections

The role of rich-club connectivity is significant in the structural property and functional behavior of complex networks. In this study, we find whether or not a very small portion of rich nodes connected to each other can strongly affect the frequency of occurrence of basic building blocks (motifs) within a heterogeneous network. Conversely whether a homogeneous network has a rich-club or not generally has no significant effect on its structure. These findings open the possibility to optimize and control the structure 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 the function of a given network.