On the rich-club effect in dense and weighted networks

TL;DR

This paper introduces a null model for dense and weighted networks to analyze the rich-club effect, addressing limitations of previous methods and enabling more accurate detection of significant network patterns.

Contribution

It proposes a new null model for dense weighted networks and generalizes the rich-club coefficient, improving pattern detection in complex networks.

Findings

Addresses randomization issues in dense unweighted graphs

Generalizes rich-club coefficient for weighted networks

Provides a method for comparing real networks with null models

Abstract

For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real--world network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the same time represents a generalization of the rich--club coefficient to weighted networks which is complementary to other recently proposed ones.