Rich-club connectivity dominates assortativity and transitivity of complex 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.
Cite
@article{arxiv.1010.1705,
title = {Rich-club connectivity dominates assortativity and transitivity of complex networks},
author = {Xiao-Ke Xu and Jie Zhang and Michael Small},
journal= {arXiv preprint arXiv:1010.1705},
year = {2015}
}
Comments
5 pages, 2 figures, accepted by Phys. Rev. E