Motif-based communities in complex networks

TL;DR

This paper introduces a motif-based framework for detecting communities in complex networks, extending traditional edge-focused methods by incorporating higher-order connectivity patterns to better understand node correlations.

Contribution

It develops a novel motif-based extension of modularity for community detection, applicable to both synthetic and real-world networks.

Findings

Motif-based modularity captures higher-order node correlations.

The framework successfully identifies communities in various networks.

Motif analysis reveals structures missed by traditional methods.

Abstract

Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman-Girvan modularity. We construct then a general framework and apply it to some synthetic and real networks.