title: 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 paid 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.
authors.affiliation: School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, People's Republic of China. xuxk@eie.polyu.edu.hk
authors.forename: Xiao-Ke
authors.initials: XK
authors.lastname: Xu
authors.forename: Jie
authors.initials: J
authors.lastname: Zhang
authors.forename: Michael
authors.initials: M
authors.lastname: Small
mesh_terms: D003196:Computer Graphics; D008962:Models, Theoretical