Perplexity-Homophily Index: Homophily through Diversity in Hypergraphs

TL;DR

This paper introduces the Perplexity-Homophily Index, a novel hyperedge-centric measure for quantifying homophily in hypergraphs by comparing observed diversity with a random baseline, capturing community and interaction patterns.

Contribution

It proposes a new hypergraph-based framework using interaction perplexity and diversity gap to measure homophily, extending traditional network analysis methods.

Findings

The index effectively captures the distribution of homophily in hypergraphs.

It reveals how homophilic and heterophilic tendencies vary with interaction size.

Experiments on synthetic and real data validate the index's utility.

Abstract

Real-world complex systems are often better modeled as hypergraphs, where edges represent group interactions involving multiple entities. Understanding and quantifying homophily (similarity-driven association) in such networks is essential for analyzing community formation and information flow. We propose a hyperedge-centric framework to quantify homophily in hypergraphs. Each interaction is represented as a hyperedge, and its interaction perplexity measures the effective number of distinct attributes it contains. Comparing this observed perplexity with a degree-preserving random baseline defines the diversity gap, which quantifies how diverse an interaction is than expected by chance. The global homophily score for a network, called Perplexity-Homophily Index, is computed by averaging the normalized diversity gap across all hyperedges. Experiments on synthetic and real-world datasets show that the proposed index captures the full distribution of homophily and reveals how homophilic and heterophilic tendencies vary with interaction size in hypergraphs.