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Access through your institution Buy or subscribe Humans tend to form groups that have a lot in common — not only the official shared interest of the group, but also characteristics such as
age, gender, political leanings or income. Sociologists and network scientists have given a lot of attention to this phenomenon, known as homophily, but most of the theoretical work is based
around networks, where links are between pairs of individuals. By contrast, in many real-world situations, the fundamental unit is the group: for instance, the group of co-authors on a
paper. Now, writing in _Science Advances_, Nate Veldt and colleagues put forward a framework for quantifying the level of homophily in group interactions, and show that simple-seeming
definitions of group homophily are constrained by combinatorics in a way that homophily on a network of pairwise interactions is not. Both these indices are subject to combinatorial
constraints that are not immediately obvious. For example, in groups with odd numbers of members, it is impossible for a system with two classes (say, two political affiliations) to have
strict majority homophily for both classes: if group compositions with at least 50% left-leaning members are all over-represented relative to the null model, for example, then groups with at
least 50% right-leaning members cannot be over-represented. These results add to the challenge of interpreting group homophily, but also make it possible to see more clearly which patterns
in real-world data can be ascribed to human behaviour. This is a preview of subscription content, access via your institution ACCESS OPTIONS Access through your institution Access Nature and
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local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support REFERENCES ORIGINAL
ARTICLE * Veldt, N., Benson, A. R. & Kleinberg, J. Combinatorial characterizations and impossibilities for higher-order homophily. _Sci. Adv._ 9, eabq3200 (2023) Article ADS Google
Scholar Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Nature Reviews Physics https://www.nature.com/natrevphys/ Zoe Budrikis Authors * Zoe Budrikis View author
publications You can also search for this author inPubMed Google Scholar CORRESPONDING AUTHOR Correspondence to Zoe Budrikis. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS
ARTICLE CITE THIS ARTICLE Budrikis, Z. Measuring similarities within groups. _Nat Rev Phys_ 5, 444 (2023). https://doi.org/10.1038/s42254-023-00624-w Download citation * Published: 02 August
2023 * Issue Date: August 2023 * DOI: https://doi.org/10.1038/s42254-023-00624-w SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable
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