{"ID":2835919,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.00107","arxiv_id":"2512.00107","title":"A Survey on Centrality and Importance Measures in Hypergraphs: Categorization and Empirical Insights","abstract":"Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs. This has led to a proliferation of specialized hypergraph centrality measures, but the field remains fragmented and lacks a unifying framework. This paper addresses this gap by providing the first systematic survey of 39 distinct measures. We introduce a novel taxonomy classifying them as: (1) structural (topology-based), (2) functional (impact on system dynamics), or (3) contextual (incorporating external features). We also present an experimental assessment comparing their empirical similarity and computation time. Finally, we discuss applications, establishing a coherent roadmap for future research in this area.","short_abstract":"Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs. This has led to a proliferation of specialized hypergraph centrality measures,...","url_abs":"https://arxiv.org/abs/2512.00107","url_pdf":"https://arxiv.org/pdf/2512.00107v1","authors":"[\"Jaewan Chun\",\"Fanchen Bu\",\"Yeongho Kim\",\"Atsushi Miyauchi\",\"Francesco Bonchi\",\"Kijung Shin\"]","published":"2025-11-27T11:06:47Z","proceeding":"physics.soc-ph","tasks":"[\"physics.soc-ph\",\"cs.SI\"]","methods":"[]","has_code":false}