{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T10:04:22Z","timestamp":1767261862066,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,2]],"date-time":"2020-02-02T00:00:00Z","timestamp":1580601600000},"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>As a more complicated network model, multilayer networks provide a better perspective for describing the multiple interactions among social networks in real life. Different from conventional community detection algorithms, the algorithms for multilayer networks can identify the underlying structures that contain various intralayer and interlayer relationships, which is of significance and remains a challenge. In this paper, aiming at the instability of the label propagation algorithm (LPA), an improved label propagation algorithm based on the SH-index (SH-LPA) is proposed. By analyzing the characteristics and deficiencies of the H-index, the SH-index is presented as an index to evaluate the importance of nodes, and the stability of the SH-LPA algorithm is verified by a series of experiments. Afterward, considering the deficiency of the existing multilayer network aggregation model, we propose an improved multilayer network aggregation model that merges two networks into a weighted single-layer network. Finally, considering the influence of the SH-index and the weight of the edge of the weighted network, a community detection algorithm (MSH-LPA) suitable for multilayer networks is exhibited in terms of the SH-LPA algorithm, and the superiority of the mentioned algorithm is verified by experimental analysis.<\/jats:p>","DOI":"10.3390\/sym12020223","type":"journal-article","created":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T01:25:51Z","timestamp":1580693151000},"page":"223","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Feasible Community Detection Algorithm for Multilayer Networks"],"prefix":"10.3390","volume":"12","author":[{"given":"Dongming","family":"Chen","sequence":"first","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, Liaoning, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panpan","family":"Du","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, Liaoning, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qianrong","family":"Jiang","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, Liaoning, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6446-8612","authenticated-orcid":false,"given":"Xinyu","family":"Huang","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, Liaoning, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongqi","family":"Wang","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, Liaoning, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,2]]},"reference":[{"key":"ref_1","unstructured":"Rozario, V.S., Chowdhury, A., and Morshed, M.S.J. (2019). Community Detection in Social Network using Temporal Data. arXiv."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1038\/35075138","article-title":"Lethality and Centrality in Protein Networks","volume":"411","author":"Jeong","year":"2001","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"026113","DOI":"10.1103\/PhysRevE.69.026113","article-title":"Finding and evaluating community structure in networks","volume":"69","author":"Newman","year":"2004","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Shiga, M., Takigawa, I., and Mamitsuka, H. (2007, January 12\u201315). A spectral clustering approach to optimally combining numericalvectors with a modular network. Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Jose, CA, USA.","DOI":"10.1145\/1281192.1281262"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.1016\/j.aml.2009.02.005","article-title":"A spectral clustering-based framework for detecting community structures in complex networks","volume":"22","author":"Jiang","year":"2009","journal-title":"Appl. Math. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"066133","DOI":"10.1103\/PhysRevE.69.066133","article-title":"Fast algorithm for detecting community structure in networks","volume":"69","author":"Newman","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_7","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"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"103018","DOI":"10.1088\/1367-2630\/12\/10\/103018","article-title":"Finding overlapping communities in networks by label propagation","volume":"12","author":"Gregory","year":"2010","journal-title":"New J. Phys."},{"key":"ref_9","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 J. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"036106","DOI":"10.1103\/PhysRevE.76.036106","article-title":"Near linear time algorithm to detect community structures in large-scale networks","volume":"76","author":"Raghavan","year":"2007","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"627581","DOI":"10.1155\/2014\/627581","article-title":"A node influence based label propagation algorithm for community detection in networks","volume":"2014","author":"Xing","year":"2014","journal-title":"Sci. World J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.physa.2015.05.080","article-title":"CenLP: A centrality-based label propagation algorithm for community detection in networks","volume":"436","author":"Sun","year":"2015","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1750162","DOI":"10.1142\/S0217984917501627","article-title":"An improved label propagation algorithm based on node importance and random walk for community detection","volume":"31","author":"Ma","year":"2017","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Berlingerio, M., Coscia, M., and Giannotti, F. (2011, January 25\u201327). Finding and characterizing communities in multidimensional networks. Proceedings of the 2011 International Conference on Advances in Social Networks Analysis and Mining, Kaohsiung, Taiwan.","DOI":"10.1109\/ASONAM.2011.104"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kazienko, P., Musial, K., Kukla, E., Kajdanowicz, T., and Br\u00f3dka, P. (2011, January 21\u201323). Multidimensional social network: Model and analysis. Proceedings of the International Conference on Computational Collective Intelligence, Gdynia, Poland.","DOI":"10.1007\/978-3-642-23935-9_37"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Rossetti, G., Berlingerio, M., and Giannotti, F. (2011, January 11). Scalable link prediction on multidimensional networks. Proceedings of the 2011 IEEE 11th International Conference on Data Mining Workshops, Vancouver, BC, Canada.","DOI":"10.1109\/ICDMW.2011.150"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Tang, L., Wang, X., and Liu, H. (2009, January 6\u20139). Uncoverning groups via heterogeneous interaction analysis. Proceedings of the 2009 Ninth IEEE International Conference on Data Mining, Miami, FL, USA.","DOI":"10.1109\/ICDM.2009.20"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1007\/s10618-013-0331-0","article-title":"Abacus: Frequent pattern mining-based community discovery in multidimensional networks","volume":"27","author":"Berlingerio","year":"2013","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_19","first-page":"011027","article-title":"Identifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systems","volume":"5","author":"Lancichinetti","year":"2015","journal-title":"Phys. Rev. X"},{"key":"ref_20","first-page":"185","article-title":"An introduction to community detection in multi -layered social network","volume":"278","author":"Filipowski","year":"2012","journal-title":"Ccis"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Kolda, T., Dunlavy, D., and Kegelmeyer, W. (2006, January 20\u201323). Multilinear algebra for analyzing data with multiple linkages. Proceedings of the Submitted to Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Philadelphia, PA, USA.","DOI":"10.2172\/883132"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Leginus, M., Dolog, P., and \u017demaitis, V. (2012, January 16\u201320). Improving tensor based recommenders with clustering. Proceedings of the International Conference on User Modeling, Adaptation, and Personalization, Montreal, QC, Canada.","DOI":"10.1007\/978-3-642-31454-4_13"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1038\/nphys2761","article-title":"Abrupt transition in the structural formation of interconnected networks","volume":"9","author":"Radicchi","year":"2013","journal-title":"Nat. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"058701","DOI":"10.1103\/PhysRevLett.111.058701","article-title":"Growing multiplex networks","volume":"111","author":"Nicosia","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","first-page":"4192","article-title":"Mathematical Formulation of Multi-Layer Networks","volume":"3","author":"Cozzo","year":"2013","journal-title":"Phys. Rev. X"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"10168","DOI":"10.1038\/ncomms10168","article-title":"The H-index of a network node and its relation to degree and coreness","volume":"7","author":"Zhou","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"16569","DOI":"10.1073\/pnas.0507655102","article-title":"An index to quantify an individual\u2019s scientific research output","volume":"102","author":"Hirsch","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_28","unstructured":"Magnani, M., Micenkova, B., and Rossi, L. (2013). Combinatorial analysis of multiple networks. arXiv."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1007\/s00265-003-0651-y","article-title":"The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations","volume":"54","author":"Lusseau","year":"2003","journal-title":"Behav. Ecol. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhu, G., and Li, K. (2014, January 12\u201314). A Unified Model for Community Detection of Multiplex Networks. Proceedings of the Web Information Systems Engineering\u2014WISE 2014, Thessaloniki, Greece.","DOI":"10.1007\/978-3-319-11749-2_3"},{"key":"ref_31","first-page":"1375","article-title":"Community Discovery Algorithm for Multi-relationship Networks","volume":"39","author":"Huang","year":"2018","journal-title":"J. North. Univ. Nat. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1126\/science.1184819","article-title":"Community Structure in Time-Dependent, Multiscale, and Multiplex Networks","volume":"328","author":"Mucha","year":"2009","journal-title":"Science"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1038\/nphys1746","article-title":"Identification of influential spreaders in complex networks","volume":"6","author":"Kitsak","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"10168","DOI":"10.1038\/ncomms10168","article-title":"The H -index of a network node and its relation to degree and coreness","volume":"7","author":"Zhou","year":"2016","journal-title":"Nat. Commu."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/223\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:54:01Z","timestamp":1760172841000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/223"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,2]]},"references-count":34,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["sym12020223"],"URL":"https:\/\/doi.org\/10.3390\/sym12020223","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,2,2]]}}}