{"paper":{"title":"Counting simplicial pairs in hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.SI","authors_text":"Aaron Smith, Fran\\c{c}ois Th\\'eberge, Jordan Barrett, Pawe{\\l} Pra{\\l}at","submitted_at":"2024-08-21T17:48:41Z","abstract_excerpt":"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 edge size increases. We then present a new Chung-Lu model that includes a parameter contr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11806","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.11806/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}