Combinatorial Characterizations and Impossibilities for Higher-order Homophily

TL;DR

This paper introduces a hypergraph-based framework to measure higher-order homophily in group interactions, revealing patterns in social data and demonstrating combinatorial impossibilities in defining such homophily.

Contribution

It develops a novel hypergraph approach for quantifying group homophily and uncovers fundamental combinatorial limitations in defining higher-order homophily.

Findings

Group homophily patterns in scientific collaboration and political co-sponsorship.

Distinct gender distributions in group photographs.

Certain natural definitions of group homophily are mathematically impossible.

Abstract

Homophily is the seemingly ubiquitous tendency for people to connect and interact with other individuals who are similar to them. This is a well-documented principle and is fundamental for how society organizes. Although many social interactions occur in groups, homophily has traditionally been measured using a graph model, which only accounts for pairwise interactions involving two individuals. Here, we develop a framework using hypergraphs to quantify homophily from group interactions. This reveals natural patterns of group homophily that appear with gender in scientific collaboration and political affiliation in legislative bill co-sponsorship, and also reveals distinctive gender distributions in group photographs, all of which cannot be fully captured by pairwise measures. At the same time, we show that seemingly natural ways to define group homophily are combinatorially impossible. This reveals important pitfalls to avoid when defining and interpreting notions of group homophily, as higher-order homophily patterns are governed by combinatorial constraints that are independent of human behavior but are easily overlooked.