Correlations between weights and overlap in ensembles of weighted multiplex networks

TL;DR

This paper develops a theoretical framework using canonical network ensembles to analyze correlations between link weights and overlaps in multiplex weighted networks, with applications to biological and social systems.

Contribution

It introduces a novel modeling approach for multiplex weighted networks incorporating weight-overlap correlations using multilinks and null models.

Findings

Framework successfully models weight-overlap correlations

Application to gene expression data demonstrates practical relevance

Null models can be constructed for diverse network structures

Abstract

Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in the multiplex networks structure, such as the overlap of the links in different layers. Many multiplex networks are also weighted, and the weights of the links can be strongly correlated with the structural properties of the multiplex network. For example in multiplex network formed by the citation and collaboration networks between PRE scientists it was found that the statistical properties of citations to co-authors are different from the one of citations to non-co-authors, i.e. the weights depend on the overlap of the links. Here we present a theoretical framework for modelling multiplex weighted networks with different types of correlations between weights and overlap. To this end, we use the framework of canonical network ensembles, and the recently introduced concept of multilinks, showing that null models of a large variety of network structures can be constructed in this way. In order to provide a concrete example of how this framework apply to real data we consider a multiplex constructed from gene expression data of healthy and cancer tissues.