{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T10:15:29Z","timestamp":1779012929792,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In network data mining, community detection refers to the problem of partitioning the nodes of a network into clusters (communities). This is equivalent to identifying the cluster label of each node. A label estimator is said to be an exact recovery of the true labels (communities) if it coincides with the true labels with a probability convergent to one. In this work, we consider the effect of label information on the exact recovery of communities in an m-uniform Hypergraph Stochastic Block Model (HSBM). We investigate two scenarios of label information: (1) a noisy label for each node is observed independently, with 1\u2212\u03b1n as the probability that the noisy label will match the true label; (2) the true label of each node is observed independently, with the probability of 1\u2212\u03b1n. We derive sharp boundaries for exact recovery under both scenarios from an information-theoretical point of view. The label information improves the sharp detection boundary if and only if \u03b1n=n\u2212\u03b2+o(1) for a constant \u03b2&gt;0.<\/jats:p>","DOI":"10.3390\/sym13112060","type":"journal-article","created":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T22:14:52Z","timestamp":1635891292000},"page":"2060","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Information Limits for Community Detection in Hypergraph with Label Information"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6245-8031","authenticated-orcid":false,"given":"Xiaofeng","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450045, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Statistics, North Dakota State University, Fargo, ND 58103, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingao","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Statistics, North Dakota State University, Fargo, ND 58103, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2283","DOI":"10.1093\/bioinformatics\/btl370","article-title":"Detecting functional modules in the yeast proteinprotein interaction network","volume":"22","author":"Chen","year":"2006","journal-title":"Bioinformatics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/00018732.2011.572452","article-title":"Analyzing and modeling real-world phenomena with complex networks: A survey of applications","volume":"60","author":"Costa","year":"2011","journal-title":"Adv. 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