  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.
