Large scale hierarchies characterize complex networks in different domains.Elements at their top, usually the most central or influential, may showmultipolarization or tend to club forming tightly interconnected communities.The rich-club phenomenon quantified this tendency based on unweighted networkrepresentations. Here, we define this metric for weighted networks and discussthe appropriate normalization which preserves nodes' strengths and discountsstructural strength-strength correlations if present. We find that in some realnetworks the results given by the weighted rich-club coefficient can be insharp contrast to the ones in the unweighted approach. We also discuss that thescanning of the weighted subgraphs formed by the high-strength hubs is able tounveil features contrary to the average: the formation of local alliances inrich-multipolarized environments, or a lack of cohesion even in the presence ofrich-club ordering. Beyond structure, this analysis matters for understandingcorrectly functionalities and dynamical processes relying on hubinterconnectedness.
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