Cohesion and segregation in higher-order networks

TL;DR

This paper explores how group size distribution and overlaps in higher-order networks influence their cohesion and segregation, revealing that increased overlaps can enhance both modularity and community formation.

Contribution

It introduces a model for higher-order networks incorporating group size and overlaps, analyzing their effects on network cohesion and segregation.

Findings

High overlap frequency increases network modularity.

Overlaps lead to tightly-knit communities.

Networks can fragment into multiple components.

Abstract

Looking to overcome the limitations of traditional networks, the network science community has lately given much attention to the so-called higher-order networks, where group interactions are modeled alongside pairwise ones. While degree distribution and clustering are the most important features of traditional network structure, higher-order networks present two additional fundamental properties that are barely addressed: the group size distribution and overlaps. Here, I investigate the impact of these properties on the network structure, focusing on cohesion and segregation (fragmentation and community formation). For that, I create artificial higher-order networks with a version of the configuration model that assigns degree to nodes and size to groups and forms overlaps with a tuning parameter $p$. Counter-intuitively, the results show that a high frequency of overlaps favors both network cohesion and segregation -- the network becomes more modular and can even break into several components, but with tightly-knit communities.