A Guide to Higher-Order Homophily

2026-06-01

AI Summary

This study addresses the challenge of characterizing and quantifying higher-order homophily and heterophily in hypergraphs by proposing the first unified framework that integrates both measurement and generative modeling. Clarifying the conceptual distinctions between higher-order mixing patterns and traditional pairwise homophily, the work establishes a comprehensive suite of metrics tailored specifically for hypergraphs. It further provides a systematic review of existing random hypergraph generative models, delineating the conditions under which each model family is appropriate. By laying a coherent theoretical foundation for the study of higher-order homophily, this research offers clear methodological guidance for future model selection and design, thereby advancing the broader field of higher-order network analysis.

Abstract

Homophily, the overrepresentation of interactions among similar individuals, and heterophily, the elevated prevalence of interactions among dissimilar ones, are frequently observed mixing patterns in social networks. As hypergraphs are increasingly used to represent social systems, a higher-order perspective on homophily and heterophily becomes ever more relevant. Here, we provide two complementary perspectives on this problem: First, we survey measures that can be used to quantify homophily (or heterophily) in hypergraphs -- emphasizing conceptual differences to existing pairwise measures -- and explain each measure through in-depth examples. Second, we provide an overview of hypergraph models for higher-order mixing patterns, distinguishing several model families with distinct use cases. By providing a guide to existing methods and synthesizing the current body of knowledge on higher-order homophily and heterophily, we lay the basis for informed methodological choices and future developments.

Problem

• homophily
• heterophily
• hypergraphs
• higher-order
• social networks

Innovation

• higher-order homophily
• hypergraphs
• heterophily
• mixing patterns
• network models