Rich-club connectivity dominates assortativity and transitivity of complex networks

TL;DR

This paper demonstrates that the connectivity among a small subset of the richest nodes in a network significantly influences the network's overall assortativity and clustering, highlighting the importance of rich-club organization.

Contribution

It reveals that rich-club connectivity can dominate network topological measures and shows how manipulating these connections can control network properties.

Findings

Rich-club connectivity influences global network measures.

Small changes in rich-club connections can alter assortativity and transitivity.

Rich-club organization explains observed biases in real-world networks.

Abstract

Rich-club, assortativity and clustering coefficients are frequently-used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network, which reveals that the rich-club connectivity is leveraged throughout the network. Our study suggests that more attention should be payed to the organization pattern of rich nodes, for the structure of a complex system as a whole is determined by the associations between the most influential individuals. Moreover, by manipulating the connectivity pattern in a very small rich-club, it is sufficient to produce a network with desired assortativity or transitivity. Conversely, our findings offer a simple explanation for the observed assortativity and transitivity in many real world networks --- such biases can be explained by the connectivities among the richest nodes.