Clustering Drives Assortativity and Community Structure in Ensembles of Networks

TL;DR

This paper investigates how clustering influences assortativity and community structure in network ensembles, revealing that clustering promotes assortativity and community formation, while high assortativity does not necessarily imply clustering.

Contribution

It uncovers the asymmetric relationship between clustering and assortativity, highlighting transitivity as a key driver over homophily in network structures.

Findings

Ensembles with strong clustering show high assortativity and community structure.

High assortativity ensembles are less biased towards clustering.

Clustering can amplify small homophilic biases.

Abstract

Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community structure, while ensembles with high assortativity are much less biased towards clustering or community structure. Further, clustered networks can amplify small homophilic bias for trait assortativity. This marked asymmetry suggests that transitivity, rather than homophily, drives the standard nonsocial/social network dichotomy.