Information theory for hypergraph similarity

TL;DR

This paper introduces an information theoretic framework for comparing hypergraphs, capturing higher-order interactions and providing scalable similarity measures validated on synthetic and real-world networks.

Contribution

It develops a normalized mutual information-based method for hypergraph similarity, extending network comparison to higher-order interactions and multiple scales.

Findings

Effective in synthetic hypergraph experiments

Reveals meaningful patterns in empirical networks

Provides a hierarchy of similarity measures

Abstract

Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network comparison are limited to pairwise interactions only. Here we construct a general information theoretic framework for hypergraph similarity, capturing meaningful correspondence among higher-order interactions while correcting for spurious correlations. Our method operationalizes any notion of structural overlap among hypergraphs as a principled normalized mutual information measure, allowing us to derive a hierarchy of increasingly granular formulations of similarity among hypergraphs within and across orders of interactions, and at multiple scales. We validate these measures through extensive experiments on synthetic hypergraphs and apply the framework to reveal meaningful patterns in a variety of empirical higher-order networks. Our work provides foundational tools for the principled comparison of higher-order networks, shedding light on the structural organization of networked systems with non-dyadic interactions.