  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.
