Measuring the higher-order homophily in a general social hypergraph

Homophily, the tendency of individuals to interact with similar others, is key to understand social dynamics. This concept has traditionally been measured in a k-uniform hypergraph model that accounts group interactions involving exactly k individuals (k ≥ 2). However, real-world interactions do not always involve the same number of individuals. Thus, in this paper, we propose a new descriptive homophily measure for general social hypergraphs where group interactions involve arbitrary number of individuals. We establish constraints of monotonic and majority homophily for two-class labels, providing a framework for analyzing homophily patterns. Experiments on several datasets reveal systematic deviations in hyperedge composition associated with node class labels relative to a label-independent baseline, offering insights into homophily pattern in complex social networks. This work bridges the gap between theoretical measures and practical applications in non-uniform hypergraphs, advancing the understanding of social and structural dynamics.