On the rich-club effect in dense and weighted networks

Abstract

For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real--world network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the same time represents a generalization of the rich--club coefficient to weighted networks which is complementary to other recently proposed ones.

Final version accepted for publication on EPJB

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• Enhanced reconstruction of weighted networks from strengths and degrees
• A Unifying Framework for Measuring Weighted Rich Clubs
• Rich-cores in networks
• Emergence of assortative mixing between clusters of cultured neurons
• The Community Structure of the Global Corporate Network
• Resilience or Robustness: Identifying Topological Vulnerabilities in Rail Networks
• Enhanced Gravity Model of trade: reconciling macroeconomic and network models
• Correlations between weights and overlap in ensembles of weighted multiplex networks
• Constrained Randomisation of Weighted Networks
• Rich-Club Ordering and the Dyadic Effect: Two Interrelated Phenomena
• Generalized Rich-Club Ordering in Networks
• Networks with arbitrary edge multiplicities
• Reduction of systemic risk by means of Pigouvian taxation
• Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal Networks
• Rich-clubness test: how to determine whether a complex network has or doesn't have a rich-club?
• Dense and sparse vertex connectivity in networks