Generalized Rich-Club Ordering in Networks

TL;DR

This paper extends the concept of rich-club ordering to include various structural and non-structural node measures, providing a framework to analyze and compare rich-club phenomena in real networks with node metadata.

Contribution

It introduces a generalized framework for rich-club ordering that encompasses diverse measures and null models, enabling comprehensive analysis of rich-club phenomena in networks.

Findings

External node metadata can validate rich-club presence.

Different measures reveal varied rich-club structures.

Framework applicable to real-world networks with metadata.

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.