A guide to higher-order homophily

Event: NetSci (2026), Boston, US

Date: 2026/06/16

Abstract

Homophily—the tendency for similar agents to interact—is a foundational mechanism shaping network structure and formation. Rooted in the social sciences [1], homophily has shaped network science broadly, motivating measures like assortativity and modularity, informing stochastic block and latent-space models, and more recently influencing graph machine learning. However, as network data increasingly record higher-order interactions—teams, group chats, collaborations, and collective problem solving—our understanding of homophily beyond pairwise ties remains underdeveloped. In higher-order representations (e.g., hypergraphs and simplicial complexes), dyadic homophily neither determines whether groups are attribute-homogeneous nor captures changes in homophily with group size. We organize this review around three questions. First, how should higher-order homophily be measured? We survey approaches that generalize homophily and related metrics (e.g., modularity) from pairwise networks to the case of hypergraphs and/or simplicial complexes (e.g., [2, 3]), as well as novel metrics unique to the higher-order setting (e.g., [4, 5]). We clarify what each measure captures, when different measures agree, and when they diverge. Second, how can one generate higher-order networks with homophily? We review generative models of higher-order networks that incorporate different notions of homophily, including higher-order stochastic block models, generalized configuration models with node attributes, and growth mechanisms with attribute-dependent attachment. Third, how does higher-order homophily affect dynamical processes? Focusing on spreading and social contagion (e.g., [6, 7]), but including other dynamics such as message passing [5], we synthesize evidence that higher-order mixing can shift thresholds and change which interventions are effective. Taken together, we hope this guide provides a common vocabulary, a map of existing methods, and practical recommendations for measuring and modeling homophily in higher-order networks.

References

[1] McPherson et al. Birds of a feather: Homophily in social networks Ann. Rev. Soc. 27:415-444 (2001)

[2] Sarker et al. Higher-order homophily on simplicial complexes PNAS 121 (12) e2315931121 (2024)

[3] Veldt et al. Combinatorial characterizations and impossibilities for higher-order homophily Sci. Adv. 9 eabq3200 (2023)

[4] Telyatnikov et al. Hypergraph neural networks through the lens of message passing TMLR (2025)

[5] Kumar et al. Perplexity-homophily index: Homophily through diversity in hypergraphs arXiv:2511.19170 (2025)

[6] Laber et al. Effects of higher-order interactions and homophily on information access inequality Comm. Phys. (2025)

[7] Rizi et al. Homophily within and across groups Nat. Comm. 16 11351 (2025)

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}
}