Statistical significance of rich-club phenomena in complex networks

Abstract

We propose that the rich-club phenomena in complex networks should be defined in the spirit of bootstrapping, in which a null model is adopted to assess the statistical significance of the rich-club detected. Our method can be served as a definition of rich-club phenomenon and is applied to analyzing three real networks and three model networks. The results improve significantly compared with previously reported results. We report a dilemma with an exceptional example, showing that there does not exist an omnipotent definition for the rich-club phenomenon.

arXiv comment3 Revtex pages + 5 figures

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• Optimizing and controlling functions of complex networks by manipulating rich-club connections
• Rich-clubness test: how to determine whether a complex network has or doesn't have a rich-club?
• Ensembles related to the rich-club coefficient for non-evolving networks
• The behavior of rich-club coefficient in scale-free networks
• Temporal rich club phenomenon and its formation mechanisms