On the rich-club effect in dense and weighted networks

Details On the rich-club effect in dense and weighted networks On the rich-club effect in dense and weighted networks

2008-07-04

arxiv.org/abs/0807.0793v2

Eur. Phys. J. B 67, 271-275 (2009).

Physics

Physics and Society

Final version accepted for publication on EPJB

Scientific paper

10.1140/epjb/e2009-00007-9

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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