{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:47:46Z","timestamp":1753876066339,"version":"3.41.2"},"reference-count":55,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,12,22]],"date-time":"2023-12-22T00:00:00Z","timestamp":1703203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,12,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>One of the longstanding challenges in network science is the identification of overlapping community structures. Real-world networks often exhibit a complex interplay of positive and negative relationships, making the recognition of overlapping communities a crucial area of research. Current community detection methods in signed networks primarily focus on discovering disjoint communities, where each node belongs exclusively to a single community. However, these algorithms often fail to detect overlapping communities, where nodes can belong to multiple communities simultaneously. To address this limitation, we propose a novel approach called Neutrosophic c-means Overlapping Community Detection (NOCD) based on neutrosophic set (NS) theory. By incorporating NS theory, our approach effectively handles the uncertainty associated with ambiguous community boundaries and appropriately handles nodes on the community boundaries and isolated nodes. The NOCD method comprises two phases: firstly, a signed graph convolutional neural network is employed to learn the structural features of the signed network in a lower-dimensional representation; secondly, overlapping communities are detected using the neutrosophic c-means algorithm applied to the embedded network. To evaluate the effectiveness of our proposed NOCD method, we conducted comprehensive experiments on both real and artificial networks. The experimental results demonstrate the effectiveness and robustness of NOCD in identifying overlapping communities, outperforming existing methods.<\/jats:p>\n               <jats:p>[Received on 3 August 2023; editorial decision on 13 December 2023; accepted on 19 December 2023]<\/jats:p>","DOI":"10.1093\/comnet\/cnad051","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T17:07:48Z","timestamp":1704992868000},"source":"Crossref","is-referenced-by-count":0,"title":["A new approach to finding overlapping community structure in signed networks based on Neutrosophic theory"],"prefix":"10.1093","volume":"12","author":[{"given":"Maryam","family":"Gholami","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Sanandaj Branch, Islamic Azad University , Pasdaran st. Sanandaj-Kurdistan , 6616935391, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0696-2900","authenticated-orcid":false,"given":"Amir","family":"Sheikhahmadi","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Sanandaj Branch, Islamic Azad University , Pasdaran st. Sanandaj-Kurdistan , 6616935391, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0792-0523","authenticated-orcid":false,"given":"Keyhan","family":"Khamforoosh","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Sanandaj Branch, Islamic Azad University , Pasdaran st. Sanandaj-Kurdistan , 6616935391, Iran"}]},{"given":"Mahdi","family":"Jalili","sequence":"additional","affiliation":[{"name":"School of Engineering, RMIT University , 124 La Trobe St , Melbourne VIC 3000, Australia"}]},{"given":"Farshid","family":"Veisi","sequence":"additional","affiliation":[{"name":"School of Engineering, RMIT University , 124 La Trobe St , Melbourne VIC 3000, Australia"}]}],"member":"286","published-online":{"date-parts":[[2024,1,11]]},"reference":[{"key":"2024011117074250900_cnad051-B1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","article-title":"The structure and function of complex networks","volume":"45","author":"Newman","year":"2003","journal-title":"SIAM review"},{"key":"2024011117074250900_cnad051-B2","doi-asserted-by":"crossref","first-page":"121269","DOI":"10.1016\/j.physa.2019.121269","article-title":"Detection of trust links on social networks using dynamic features","volume":"527","author":"Golzardi","year":"2019","journal-title":"Physica A"},{"key":"2024011117074250900_cnad051-B3","doi-asserted-by":"crossref","first-page":"127359","DOI":"10.1016\/j.physa.2022.127359","article-title":"Overlapping community detection in networks based on Neutrosophic theory","volume":"598","author":"Gholami","year":"2022","journal-title":"Physica A"},{"key":"2024011117074250900_cnad051-B4","doi-asserted-by":"crossref","first-page":"7821","DOI":"10.1073\/pnas.122653799","article-title":"Community structure in social and biological networks","volume":"99","author":"Girvan","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2024011117074250900_cnad051-B5","doi-asserted-by":"crossref","first-page":"7821","DOI":"10.1073\/pnas.122653799","article-title":"Community structure in social and biological networks","volume":"99","author":"Girvan","year":"2002","journal-title":"Proceedings of the national academy of sciences"},{"key":"2024011117074250900_cnad051-B6","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1307\/mmj\/1028989917","article-title":"On the notion of balance of a signed graph","volume":"2","author":"Harary","year":"1953","journal-title":"Michigan Mathematical Journal"},{"key":"2024011117074250900_cnad051-B7","first-page":"1","article-title":"A survey of signed network mining in social media","volume":"49","author":"Tang","year":"2016","journal-title":"ACM Computing Surveys (CSUR"},{"first-page":"1505","year":"2016","author":"Chu","key":"2024011117074250900_cnad051-B8"},{"key":"2024011117074250900_cnad051-B9","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1109\/TCBB.2015.2401014","article-title":"Detecting protein complexes from signed protein-protein interaction networks","volume":"12","author":"Ou-Yang","year":"2015","journal-title":"IEEE\/ACM transactions on computational biology and bioinformatics"},{"key":"2024011117074250900_cnad051-B10","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/ASONAM.2012.48","volume-title":"2012 IEEE\/ACM International Conference on Advances in Social Networks Analysis and Mining","author":"Anchuri","year":"2012"},{"key":"2024011117074250900_cnad051-B11","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s00500-013-1060-4","article-title":"A comparative analysis of evolutionary and memetic algorithms for community detection from signed social networks","volume":"18","author":"Li","year":"2014","journal-title":"Soft Computing"},{"key":"2024011117074250900_cnad051-B12","doi-asserted-by":"crossref","first-page":"016114","DOI":"10.1103\/PhysRevE.80.016114","article-title":"Analysis of community structure in networks of correlated data","volume":"80","author":"G\u00f3mez","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2024011117074250900_cnad051-B13","doi-asserted-by":"crossref","first-page":"036115","DOI":"10.1103\/PhysRevE.80.036115","article-title":"Community detection in networks with positive and negative links","volume":"80","author":"Traag","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2024011117074250900_cnad051-B14","first-page":"559","volume-title":"Proceedings of the 2010 SIAM International Conference on Data Mining","author":"Kunegis","year":"2010"},{"first-page":"615","year":"2012","author":"Chiang","key":"2024011117074250900_cnad051-B15"},{"key":"2024011117074250900_cnad051-B16","first-page":"P03021","article-title":"Overlapping community detection in networks with positive and negative links","volume":"2014","author":"Chen","year":"2014","journal-title":"Theory and Experiment"},{"key":"2024011117074250900_cnad051-B17","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1109\/TKDE.2017.2700304","article-title":"Stochastic blockmodeling and variational Bayes learning for signed network analysis","volume":"29","author":"Yang","year":"2017","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"key":"2024011117074250900_cnad051-B18","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1109\/JSYST.2017.2775613","article-title":"Community mining in signed networks based on dynamic mechanism","volume":"13","author":"Chen","year":"2017","journal-title":"IEEE Systems Journal"},{"key":"2024011117074250900_cnad051-B19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.socnet.2008.08.001","article-title":"Partitioning signed social networks","volume":"31","author":"Doreian","year":"2009","journal-title":"Soc. Netw"},{"first-page":"1088","year":"2019","author":"Cucuringu","key":"2024011117074250900_cnad051-B20"},{"key":"2024011117074250900_cnad051-B21","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1038\/nature03607","article-title":"Uncovering the overlapping community structure of complex networks in nature and society","volume":"435","author":"Palla","year":"2005","journal-title":"Nature"},{"first-page":"726","year":"2021","author":"Wang","key":"2024011117074250900_cnad051-B22"},{"issue":"7307","key":"2024011117074250900_cnad051-B23","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1038\/nature09182","article-title":"Link communities reveal multiscale complexity in networks","volume":"466","author":"Ahn","year":"2010","journal-title":"Nature"},{"first-page":"19","year":"2013","author":"Shen","key":"2024011117074250900_cnad051-B24"},{"first-page":"115","year":"2016","author":"Wang","key":"2024011117074250900_cnad051-B25"},{"key":"2024011117074250900_cnad051-B26","doi-asserted-by":"crossref","first-page":"e0178046","DOI":"10.1371\/journal.pone.0178046","article-title":"An efficient semi-supervised community detection framework in social networks","volume":"12","author":"Li","year":"2017","journal-title":"PloS one"},{"first-page":"869","year":"2017","author":"Hoang","key":"2024011117074250900_cnad051-B27"},{"key":"2024011117074250900_cnad051-B28","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s11036-017-0883-0","article-title":"Community detection based on regularized semi-nonnegative matrix tri-factorization in signed networks","volume":"23","author":"Li","year":"2018","journal-title":"Mobile Networks and Applications"},{"first-page":"1608","year":"2015","author":"Shahriari","key":"2024011117074250900_cnad051-B29"},{"key":"2024011117074250900_cnad051-B30","doi-asserted-by":"crossref","first-page":"2274","DOI":"10.1109\/TCYB.2014.2305974","article-title":"A multiobjective evolutionary algorithm based on similarity for community detection from signed social networks","volume":"44","author":"Liu","year":"2014","journal-title":"IEEE transactions on cybernetics"},{"key":"2024011117074250900_cnad051-B31","doi-asserted-by":"crossref","DOI":"10.1142\/2895","volume-title":"Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers","author":"Zadeh","year":"1996"},{"key":"2024011117074250900_cnad051-B32","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-29127-2","volume-title":"On Intuitionistic Fuzzy Sets Theory","author":"Atanassov","year":"2012"},{"key":"2024011117074250900_cnad051-B33","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3472-7","volume-title":"Statistical Reasoning with Imprecise Probabilities","author":"Walley","year":"1991"},{"volume-title":"A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability: Neutrsophic Logic","year":"2005","author":"Smarandache","key":"2024011117074250900_cnad051-B34"},{"volume-title":"Neutrosophic logic and set","year":"1995","author":"Smarandache","key":"2024011117074250900_cnad051-B35"},{"key":"2024011117074250900_cnad051-B36","doi-asserted-by":"crossref","first-page":"179","DOI":"10.3390\/sym9090179","article-title":"NS-k-NN: neutrosophic set-based k-nearest neighbors classifier","volume":"9","author":"Akbulut","year":"2017","journal-title":"Symmetry"},{"key":"2024011117074250900_cnad051-B37","doi-asserted-by":"crossref","first-page":"2710","DOI":"10.1016\/j.patcog.2015.02.018","article-title":"NCM: neutrosophic c-means clustering algorithm","volume":"48","author":"Guo","year":"2015","journal-title":"Patt. Recogn"},{"key":"2024011117074250900_cnad051-B38","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.patcog.2008.10.002","article-title":"New neutrosophic approach to image segmentation","volume":"42","author":"Guo","year":"2009","journal-title":"Patt. Recogn"},{"key":"2024011117074250900_cnad051-B39","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1049\/iet-ipr.2015.0738","article-title":"Scheme for unsupervised colour\u2013texture image segmentation using neutrosophic set and non-subsampled contourlet transform","volume":"10","author":"Heshmati","year":"2016","journal-title":"IET Image Process"},{"volume-title":"Some Neutrosophic Algebraic Dtructures and Neutrosophic N-algebraic Structures","year":"2006","author":"Kandasamy","key":"2024011117074250900_cnad051-B40"},{"year":"1973","author":"Dunn","key":"2024011117074250900_cnad051-B41"},{"key":"2024011117074250900_cnad051-B42","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0098-3004(84)90020-7","article-title":"FCM: the fuzzy c-means clustering algorithm","volume":"10","author":"Bezdek","year":"1984","journal-title":"Comput. Geosci"},{"volume-title":"Pattern Recognition with Fuzzy Objective Function Algorithms","year":"2013","author":"Bezdek","key":"2024011117074250900_cnad051-B43"},{"first-page":"97","year":"2005","author":"Wang","key":"2024011117074250900_cnad051-B44"},{"key":"2024011117074250900_cnad051-B45","doi-asserted-by":"crossref","first-page":"7811","DOI":"10.37418\/amsj.9.10.13","article-title":"De-neutrosophication technique of single valued linear heptagonal neutrosophic number","volume":"9","author":"Richard","year":"2005","journal-title":"Adv. Math., Sci. J"},{"key":"2024011117074250900_cnad051-B46","first-page":"2710","article-title":"NCM: neutrosophic c-means clustering algorithm","author":"Guo","year":"2015"},{"key":"2024011117074250900_cnad051-B47","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1109\/TKDE.2018.2849727","article-title":"A survey on network embedding","volume":"31","author":"Cui","year":"2018","journal-title":"IEEE Trans. Knowl Data Eng"},{"first-page":"929","year":"2018","author":"Derr","key":"2024011117074250900_cnad051-B48"},{"key":"2024011117074250900_cnad051-B49","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/00223980.1946.9917275","article-title":"Attitudes and cognitive organization","volume":"21","author":"Heider","year":"1946","journal-title":"J. Psychol"},{"key":"2024011117074250900_cnad051-B50","article-title":"Inductive representation learning on large graphs","volume":"30","author":"Hamilton","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst"},{"key":"2024011117074250900_cnad051-B51","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1109\/TKDE.2007.1061","article-title":"Community mining from signed social networks","volume":"19","author":"Yang","year":"2007","journal-title":"IEEE Trans. Knowl. Data Eng"},{"key":"2024011117074250900_cnad051-B52","doi-asserted-by":"crossref","first-page":"046110","DOI":"10.1103\/PhysRevE.78.046110","article-title":"Benchmark graphs for testing community detection algorithms","volume":"78","author":"Lancichinetti","year":"2008","journal-title":"Phys. Rev. E"},{"key":"2024011117074250900_cnad051-B53","doi-asserted-by":"crossref","first-page":"2274","DOI":"10.1109\/TCYB.2014.2305974","article-title":"A multiobjective evolutionary algorithm based on similarity for community detection from signed social networks","volume":"44","author":"Liu","year":"2014","journal-title":"IEEE Trans. Cybern"},{"key":"2024011117074250900_cnad051-B54","doi-asserted-by":"crossref","first-page":"033015","DOI":"10.1088\/1367-2630\/11\/3\/033015","article-title":"Detecting the overlapping and hierarchical community structure in complex networks","volume":"11","author":"Lancichinetti","year":"2009","journal-title":"New journal of physics"},{"key":"2024011117074250900_cnad051-B55","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/j.1834-4461.1952.tb00565.x","article-title":"Nama cult of the central highlands, New Guinea","volume":"23","author":"Read","year":"1952","journal-title":"Oceania"}],"container-title":["Journal of Complex Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/12\/1\/cnad051\/55452104\/cnad051.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/12\/1\/cnad051\/55452104\/cnad051.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T17:08:17Z","timestamp":1704992897000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comnet\/article\/doi\/10.1093\/comnet\/cnad051\/7516437"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,22]]},"references-count":55,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,12,22]]}},"URL":"https:\/\/doi.org\/10.1093\/comnet\/cnad051","relation":{},"ISSN":["2051-1329"],"issn-type":[{"type":"electronic","value":"2051-1329"}],"subject":[],"published-other":{"date-parts":[[2024,2,1]]},"published":{"date-parts":[[2023,12,22]]},"article-number":"cnad051"}}