{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T01:33:27Z","timestamp":1760578407418,"version":"3.44.0"},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,8,17]],"date-time":"2025-08-17T00:00:00Z","timestamp":1755388800000},"content-version":"vor","delay-in-days":52,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present two ways to measure the simplicial nature of a hypergraph: the simplicial ratio and the simplicial matrix. We show that the simplicial ratio captures the frequency, as well as the rarity, of simplicial interactions in a hypergraph while the simplicial matrix provides more fine-grained details. We then compute the simplicial ratio, as well as the simplicial matrix, for 10 real-world hypergraphs and, from the data collected, hypothesize that simplicial interactions are more and more deliberate as hyperedge size increases. We then present a new Chung-Lu model that includes a parameter controlling (in expectation) the frequency of simplicial interactions. We use this new model, as well as the real-world hypergraphs, to show that multiple stochastic processes exhibit different behaviour when performed on simplicial hypergraphs vs. non-simplicial hypergraphs.<\/jats:p>","DOI":"10.1093\/comnet\/cnaf021","type":"journal-article","created":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T07:56:53Z","timestamp":1751529413000},"source":"Crossref","is-referenced-by-count":1,"title":["Counting simplicial pairs in hypergraphs"],"prefix":"10.1093","volume":"13","author":[{"given":"Jordan","family":"Barrett","sequence":"first","affiliation":[{"name":"Department of Mathematics, Toronto Metropolitan University , Toronto, ON, M5B 2K3,","place":["Canada"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9176-8493","authenticated-orcid":false,"given":"Pawe\u0142","family":"Pra\u0142at","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Toronto Metropolitan University , Toronto, ON, M5B 2K3,","place":["Canada"]}]},{"given":"Aaron","family":"Smith","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Ottawa , Ottawa, ON, K1N 6N5,","place":["Canada"]}]},{"given":"Fran\u00e7ois","family":"Th\u00e9berge","sequence":"additional","affiliation":[{"name":"Tutte Institute for Mathematics and Computing , Ottawa, ON, K1G 3Z4,","place":["Canada"]}]}],"member":"286","published-online":{"date-parts":[[2025,8,17]]},"reference":[{"key":"2025081709215970600_cnaf021-B1","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1111\/j.1749-6632.1979.tb17777.x","article-title":"On properties of a well-known graph or what is your Ramsey number","volume":"328","author":"Odda","year":"1979","journal-title":"Ann N Y Acade Sci"},{"key":"2025081709215970600_cnaf021-B2","doi-asserted-by":"crossref","first-page":"1301994","DOI":"10.3389\/fphy.2023.1301994","article-title":"Hypergraph patterns and collaboration 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