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For many complex networks present in nature only a single instance, usuallyof large size, is available. Any measurement made on this single instancecannot be repeated on different realizations. In order to detect significantpatterns in a real--world network it is therefore crucial to compare themeasured results with a null model counterpart. Here we focus on dense andweighted networks, proposing a suitable null model and studying the behaviourof the degree correlations as measured by the rich-club coefficient. Our methodsolves an existing problem with the randomization of dense unweighted graphs,and at the same time represents a generalization of the rich--club coefficientto weighted networks which is complementary to other recently proposed ones.

On the rich-club effect in dense and weighted networks