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arXiv · 0807.0793

On the rich-club effect in dense and weighted networks

Vinko Zlatic·Ginestra Bianconi·Albert Diaz-Guilera·Diego Garlaschelli·Francesco Rao·Guido Caldarelli
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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.

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Vinko Zlatic, Ginestra Bianconi, Albert Diaz-Guilera, Diego Garlaschelli, Francesco Rao, Guido Caldarelli. 2009-01-09. On the rich-club effect in dense and weighted networks. https://doi.org/10.1140/epjb/e2009-00007-9

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