{"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/three-hypergraph-eigenvector-centralities","title":"Three hypergraph eigenvector centralities","arxiv_id":"1807.09644","date":"2018-07-25","proceeding":null,"authors":["Austin R. Benson"],"abstract":"Eigenvector centrality is a standard network analysis tool for determining\nthe importance of (or ranking of) entities in a connected system that is\nrepresented by a graph. However, many complex systems and datasets have natural\nmulti-way interactions that are more faithfully modeled by a hypergraph. Here\nwe extend the notion of graph eigenvector centrality to uniform hypergraphs.\nTraditional graph eigenvector centralities are given by a positive eigenvector\nof the adjacency matrix, which is guaranteed to exist by the Perron-Frobenius\ntheorem under some mild conditions. The natural representation of a hypergraph\nis a hypermatrix (colloquially, a tensor). Using recently established\nPerron-Frobenius theory for tensors, we develop three tensor eigenvectors\ncentralities for hypergraphs, each with different interpretations. We show that\nthese centralities can reveal different information on real-world data by\nanalyzing hypergraphs constructed from n-gram frequencies, co-tagging on stack\nexchange, and drug combinations observed in patient emergency room visits.","url_abs":"http://arxiv.org/abs/1807.09644v3","url_pdf":"http://arxiv.org/pdf/1807.09644v3.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":"abstracts"},"code_links":[{"paper_slug":"three-hypergraph-eigenvector-centralities","repo_url":"https://github.com/arbenson/Hyper-Evec-Centrality","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.09644","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}