Rich-club vs rich-multipolarization phenomena in weighted networks

Abstract

Large scale hierarchies characterize complex networks in different domains. Elements at their top, usually the most central or influential, may show multipolarization or tend to club forming tightly interconnected communities. The rich-club phenomenon quantified this tendency based on unweighted network representations. Here, we define this metric for weighted networks and discuss the appropriate normalization which preserves nodes' strengths and discounts structural strength-strength correlations if present. We find that in some real networks the results given by the weighted rich-club coefficient can be in sharp contrast to the ones in the unweighted approach. We also discuss that the scanning of the weighted subgraphs formed by the high-strength hubs is able to unveil features contrary to the average: the formation of local alliances in rich-multipolarized environments, or a lack of cohesion even in the presence of rich-club ordering. Beyond structure, this analysis matters for understanding correctly functionalities and dynamical processes relying on hub interconnectedness.

12 pages, 2 figures

References in corpus (4)

• Finding community structure in networks using the eigenvectors of matrices
• The Rich-Club Phenomenon In The Internet Topology
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• Correlations in weighted networks

Cited by in corpus (5)

• Prominence and control: The weighted rich-club effect
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• On the rich-club effect in dense and weighted networks
• The World-Trade Web: Topological Properties, Dynamics, and Evolution
• Ensembles related to the rich-club coefficient for non-evolving networks