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PreprintCC BY 4.0arXiv

A Guide to Higher-Order Homophily

  • Moritz Laber
  • Brennan Klein
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Abstract

Homophily, the overrepresentation of interactions among similar individuals, and heterophily, the elevated prevalence of interactions among dissimilar ones, are frequently observed mixing patterns in social networks. As hypergraphs are increasingly used to represent social systems, a higher-order perspective on homophily and heterophily becomes ever more relevant. Here, we provide two complementary perspectives on this problem: First, we survey measures that can be used to quantify homophily (or heterophily) in hypergraphs -- emphasizing conceptual differences to existing pairwise measures -- and explain each measure through in-depth examples. Second, we provide an overview of hypergraph models for higher-order mixing patterns, distinguishing several model families with distinct use cases. By providing a guide to existing methods and synthesizing the current body of knowledge on higher-order homophily and heterophily, we lay the basis for informed methodological choices and future developments.

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Cite

BibTeXRIS
BibTeX
@misc{laber2026guide,
  title = {{A Guide to Higher-Order Homophily}},
  author = {Moritz Laber and Brennan Klein},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.02537},
  eprint = {2606.02537},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.02537},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Guide to Higher-Order Homophily
AU  - Moritz Laber
AU  - Brennan Klein
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2606.02537
UR  - https://arxiv.org/abs/2606.02537
AB  - Homophily, the overrepresentation of interactions among similar individuals, and heterophily, the elevated prevalence of interactions among dissimilar ones, are frequently observed mixing patterns in social networks. As hypergraphs are increasingly used to represent social systems, a higher-order perspective on homophily and heterophily becomes ever more relevant. Here, we provide two complementary perspectives on this problem: First, we survey measures that can be used to quantify homophily (or heterophily) in hypergraphs -- emphasizing conceptual differences to existing pairwise measures -- and explain each measure through in-depth examples. Second, we provide an overview of hypergraph models for higher-order mixing patterns, distinguishing several model families with distinct use cases. By providing a guide to existing methods and synthesizing the current body of knowledge on higher-order homophily and heterophily, we lay the basis for informed methodological choices and future developments.
ER  -