Generalized rich-club ordering in networks

Rich-club ordering refers to the tendency of nodes with a high degree to be more interconnected than expected. In this article, we consider the concept of rich-club ordering when generalized to structural measures that differ from the node degree and to non-structural measures (i.e. to node metadata). The differences in considering rich-club ordering with respect to both structural and non-structural measures is then discussed in terms of employed coefficients and of appropriate null models (link rewiring vs. metadata reshuffling). Once a framework for the evaluation of generalized rich-club ordering is defined, we investigate such a phenomenon in real networks provided with node metadata. By considering different notions of node richness, we compare structural and non-structural rich-club ordering, observing how external information about the network nodes is able to validate the presence of rich-clubs in networked systems.