A unifying framework for measuring weighted rich clubs.

Network analysis can help uncover meaningful regularities in the organization of complex systems. Among these, rich clubs are a functionally important property of a variety of social, technological and biological networks. Rich clubs emerge when nodes that are somehow prominent or 'rich' (e.g., highly connected) interact preferentially with one another. The identification of rich clubs is non-trivial, especially in weighted networks, and to this end multiple distinct metrics have been proposed. Here we describe a unifying framework for detecting rich clubs which intuitively generalizes various metrics into a single integrated method. This generalization rests upon the explicit incorporation of randomized control networks into the measurement process. We apply this framework to real-life examples, and show that, depending on the selection of randomized controls, different kinds of rich-club structures can be detected, such as topological and weighted rich clubs.J.A. is supported by the NIH-Oxford-Cambridge Scholarship Program. P.P. is employed by Queen Mary University of London. M.R. is supported by the NARSAD Young Investigator and Isaac Newton Trust grants. E.T.B. is employed half-time by the University of Cambridge, UK, and half-time by GlaxoSmithKline (GSK). P.E.V. is supported by the Medical Research Council (grant number MR/K020706/1).This is the final version of the article. It first appeared from NPG via http://dx.doi.org/10.1038/srep0725