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Title: Rich-club connectivity dominates assortativity and transitivity of complex networks
Authors: Xu, X
Zhang, J
Small, M
Issue Date: Oct-2010
Source: Physical review. E, Statistical, nonlinear, and soft matter physics, Oct. 2010, v. 82, no. 4, 046117, p. 1-4
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.
Keywords: Complex networks
Topology
Publisher: American Physical Society
Journal: Physical review. E, Statistical, nonlinear, and soft matter physics 
ISSN: 1539-3755
EISSN: 1550-2376
DOI: 10.1103/PhysRevE.82.046117
Rights: Physical Review E © 2010 The American Physical Society. The Journal's web site is located at http://pre.aps.org/
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