Friend-of-Friend Generative Model for Group Interactions

Generative models of network formation can offer heuristic explanations for microscopic mechanisms that give rise to the large-scale structures observed in empirical data. Yet, most existing models generate pairwise networks, while many social and physical systems involve interactions in groups. Here, we extend the friend-of-friend (FoF), also known as the triadic closure mechanism to hypergraph growth. The process relies on simple local rules describing how groups of pre-existing and newly arriving nodes form over time. Analytical results and simulations show that higher-order interactions broaden the degree distribution, increase edge overlaps, and induce a rich-club ordering absent in purely dyadic settings. We also show that increasing interaction order reorganizes community structure, yielding fewer communities at comparable modularity scores. Additionally, we calibrate our model on two empirical group-interaction datasets and benchmark it against a standard degree-driven growth baseline. The baseline better matches the extreme tail of the degree distribution, whereas the FoF model more accurately reproduces edge-overlap distributions and more closely matches the empirical community organization.