Perplexity-Homophily Index: Homophily through Diversity in Hypergraphs

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.