Title: Generalized Rich-Club Ordering in Networks,
Abstract: Rich-club ordering refers to the tendency of nodes with a high degree to be
more interconnected than expected. In this paper 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 (RCO) 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 (GRCO) 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.