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In this paper, we focus on inclusion within higher-order networks, referring to situations where specific entities participate in an interaction, and subsets of those entities also interact with each other. Traditional modeling approaches to higher-order networks tend to either not consider inclusion at all (e.g., hypergraph models) or explicitly assume perfect and complete inclusion (e.g., simplicial complex models). To allow for a more nuanced assessment of inclusion in higher-order networks, we introduce the concept of \u201csimpliciality\u201d and several corresponding measures. Contrary to current modeling practice, we show that empirically observed systems rarely lie at either end of the simpliciality spectrum. In addition, we show that generative models fitted to these datasets struggle to capture their inclusion structure. These findings suggest new modeling directions for the field of higher-order network science.<\/jats:p>","DOI":"10.1140\/epjds\/s13688-024-00458-1","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T12:19:43Z","timestamp":1709813983000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["The simpliciality of higher-order networks"],"prefix":"10.1140","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1270-4980","authenticated-orcid":false,"given":"Nicholas W.","family":"Landry","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4464-2692","authenticated-orcid":false,"given":"Jean-Gabriel","family":"Young","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4789-2275","authenticated-orcid":false,"given":"Nicole","family":"Eikmeier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"issue":"9","key":"458_CR1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0136497","volume":"10","author":"R Mastrandrea","year":"2015","unstructured":"Mastrandrea R, Fournet J, Barrat A (2015) Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys. 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