Perplexity-Homophily Index: Homophily through Diversity in Hypergraphs

2025-11-24

AI Summary

This paper addresses the challenge of quantifying homophily—i.e., the tendency of similar nodes to co-occur in group interactions—in hypergraphs. Methodologically, it introduces the first hyperedge-centric homophily analysis framework grounded in perplexity: it defines *interaction perplexity* to measure attribute diversity within hyperedges and constructs a degree-preserving randomized baseline; homophily is then quantified via a normalized “diversity gap,” yielding a global *Perplexity-Homophily* index. Its key contribution lies in pioneering the use of perplexity for hypergraph homophily modeling, enabling sensitive detection of dynamic homophilous or heterophilous tendencies across hyperedges of varying sizes. Experiments on synthetic and real-world hypergraphs demonstrate that the proposed index accurately characterizes homophily distribution patterns and size-dependent trends, significantly outperforming existing pairwise-relation-based metrics.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Quantifying homophily in hypergraph group interactions
• Measuring diversity gap between observed and random interactions
• Analyzing homophilic tendencies across varying hyperedge sizes

Innovation

• Hyperedge-centric framework for homophily quantification
• Interaction perplexity measures effective attribute diversity
• Perplexity-Homophily Index averages normalized diversity gaps