Statistical significance of rich-club phenomena in complex networks

TL;DR

This paper introduces a bootstrap-based statistical method to assess the significance of rich-club phenomena in complex networks, providing a more rigorous definition and analysis compared to previous approaches.

Contribution

It proposes a new statistical framework for defining and testing rich-club phenomena, applied to real and model networks, revealing limitations of existing definitions.

Findings

Significant improvement over previous results

Application to multiple real and model networks

Identification of limitations in existing rich-club definitions

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.