Generalizing Homophily to Simplicial Complexes

Abstract: Group interactions occur frequently in social settings, yet their properties beyond pairwise relationships in network models remain unexplored. In this work, we study homophily, the nearly ubiquitous phenomena wherein similar individuals are more likely than random to form connections with one another, and define it on simplicial complexes, a generalization of network models that goes beyond dyadic interactions. While some group homophily definitions have been proposed in the literature, we provide theoretical and empirical evidence that prior definitions mostly inherit properties of homophily in pairwise interactions rather than capture the homophily of group dynamics. Hence, we propose a new measure, $k$-simplicial homophily, which properly identifies homophily in group dynamics. Across 16 empirical networks, $k$-simplicial homophily provides information uncorrelated with homophily measures on pairwise interactions. Moreover, we show the empirical value of $k$-simplicial homophily in identifying when metadata on nodes is useful for predicting group interactions, whereas previous measures are uninformative.