Optimizing and controlling functions of complex networks by manipulating rich-club connections

TL;DR

This paper demonstrates that manipulating rich-club connections in complex networks can significantly influence their structural motifs and functions, offering new ways to optimize and control network behavior.

Contribution

It reveals the impact of rich-club connectivity on network function and introduces a new method to identify rich-club presence based on subgraph ratios.

Findings

Rich-club connections affect motif frequency in heterogeneous networks.

Manipulating rich-club links can optimize network function.

A new subgraph ratio profile method for detecting rich-clubs.

Abstract

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.