{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hypercore-decomposition-for-non-fragile","title":"Hypercore Decomposition for Non-Fragile Hyperedges: Concepts, Algorithms, Observations, and Applications","arxiv_id":"2301.08440","date":"2023-01-20","proceeding":null,"authors":["Fanchen Bu","Geon Lee","Kijung Shin"],"abstract":"Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the notion of $k$-cores, which proved useful with numerous applications for pairwise graphs, to hypergraphs. However, the previous extensions are based on an unrealistic assumption that hyperedges are fragile, i.e., a high-order relation becomes obsolete as soon as a single member leaves it. In this work, we propose a new substructure model, called ($k$, $t$)-hypercore, based on the assumption that high-order relations remain as long as at least $t$ fraction of the members remain. Specifically, it is defined as the maximal subhypergraph where (1) every node is contained in at least $k$ hyperedges in it and (2) at least $t$ fraction of the nodes remain in every hyperedge. We first prove that, given $t$ (or $k$), finding the ($k$, $t$)-hypercore for every possible $k$ (or $t$) can be computed in time linear w.r.t the sum of the sizes of hyperedges. Then, we demonstrate that real-world hypergraphs from the same domain share similar ($k$, $t$)-hypercore structures, which capture different perspectives depending on $t$. Lastly, we show the successful applications of our model in identifying influential nodes, dense substructures, and vulnerability in hypergraphs.","url_abs":"https://arxiv.org/abs/2301.08440v2","url_pdf":"https://arxiv.org/pdf/2301.08440v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"hypercore-decomposition-for-non-fragile","repo_url":"https://github.com/bokveizen/non-fragile-hypercore","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}