{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T14:56:23Z","timestamp":1775228183648,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T00:00:00Z","timestamp":1608768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201806175006"],"award-info":[{"award-number":["201806175006"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972174"],"award-info":[{"award-number":["61972174"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Guangdong Premier Key-Discipline Enhancement Scheme","award":["2016GDYSZDXK036"],"award-info":[{"award-number":["2016GDYSZDXK036"]}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R35-GM126985"],"award-info":[{"award-number":["R35-GM126985"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A community in a complex network refers to a group of nodes that are densely connected internally but with only sparse connections to the outside. Overlapping community structures are ubiquitous in real-world networks, where each node belongs to at least one community. Therefore, overlapping community detection is an important topic in complex network research. This paper proposes an overlapping community detection algorithm based on membership degree propagation that is driven by both global and local information of the node community. In the method, we introduce a concept of membership degree, which not only stores the label information, but also the degrees of the node belonging to the labels. Then the conventional label propagation process could be extended to membership degree propagation, with the results mapped directly to the overlapping community division. Therefore, it obtains the partition result and overlapping node identification simultaneously and greatly reduces the computational time. The proposed algorithm was applied to a synthetic Lancichinetti\u2013Fortunato\u2013Radicchi (LFR) dataset and nine real-world datasets and compared with other up-to-date algorithms. The experimental results show that our proposed algorithm is effective and outperforms the comparison methods on most datasets. Our proposed method significantly improved the accuracy and speed of the overlapping node prediction. It can also substantially alleviate the computational complexity of community structure detection in general.<\/jats:p>","DOI":"10.3390\/e23010015","type":"journal-article","created":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T09:02:44Z","timestamp":1608800564000},"page":"15","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Overlapping Community Detection Based on Membership Degree Propagation"],"prefix":"10.3390","volume":"23","author":[{"given":"Rui","family":"Gao","sequence":"first","affiliation":[{"name":"Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shoufeng","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5115-8137","authenticated-orcid":false,"given":"Xiaohu","family":"Shi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Changchun 130012, China"},{"name":"Zhuhai Laboratory of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Zhuhai College of Jilin University, Zhuhai 519041, China"},{"name":"Department of Electrical Engineering and Computer Science, Informatics Institute, and Christopher S. Bond Life Sciences Center, University of Missouri, Columbia, MO 65211, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanchun","family":"Liang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Changchun 130012, China"},{"name":"Zhuhai Laboratory of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Zhuhai College of Jilin University, Zhuhai 519041, China"},{"name":"Department of Electrical Engineering and Computer Science, Informatics Institute, and Christopher S. 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