Mixing Patterns in Higher-Order Networks: A Review

Event: IC2S2 (2026), Burlington, US

Date: 2026/07/31

Abstract

Homophily, the tendency for similar agents to interact, is a foundational mechanism shaping network structure and formation. Having conceptual roots in the social sciences, it has been mathematically formalized in different ways leading to an abundance of measures employable in network analysis and generative models of networks that attempt to create networks aligned with a given definition. However, as network data increasingly record higher-order interactions, e.g., teams and group chats, our understanding of homophily beyond pairwise ties remains underdeveloped. In higher-order representations of social networks (e.g., hypergraphs), dyadic homophily neither determines whether groups are attribute-homogeneous nor captures changes in homophily with group size. Here, we review the current state of homophily in higher-order networks and provide a pedagogical introduction to the subject of homophily. We organize our review around three questions: First, how should higher-order homophily be measured? We review generalizations of existing measures on pairwise networks to the higher-order setting, as well as novel homophily measures unique to hypergraphs or simplicial complexes. Second, how can one generate higher-order networks with homophily? We establish a taxonomy of generative models for higher-order networks with homophily and discuss computational challenges. And third, how does higher-order homophily affect dynamical processes on higher-order networks? We summarize evidence that higher-order homophily shapes various dynamical processes, e.g., by shifting critical points and changing which interventions are effective. Taken together, we hope this review provides a common vocabulary, a map of existing methods, and practical recommendations for measuring and modeling homophily in higher-order networks.

Slides

When using these materials, please cite:

@misc{laber2026_guidehigherorderhomophily,
  title = {A Guide to Higher-Order Homophily},
  author = {Laber, Moritz and Klein, Brennan},
  year = 2026,
  archiveprefix = {arXiv}
  eprint = {2606.02537},
  doi = {10.48550/arXiv.2606.02537}
}