{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T02:08:21Z","timestamp":1783649301632,"version":"3.55.0"},"reference-count":65,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,15]],"date-time":"2020-04-15T00:00:00Z","timestamp":1586908800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Liaoning Natural Science Foundation","award":["No.20170540320"],"award-info":[{"award-number":["No.20170540320"]}]},{"name":"the Doctoral Scientific Research Foundation of Liaoning Province","award":["No. 20170520358"],"award-info":[{"award-number":["No. 20170520358"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61473073"],"award-info":[{"award-number":["No. 61473073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["Nos. N161702001, N2017010 and N172410005-2"],"award-info":[{"award-number":["Nos. N161702001, N2017010 and N172410005-2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Social network analysis is a multidisciplinary research covering informatics, mathematics, sociology, management, psychology, etc. In the last decade, the development of online social media has provided individuals with a fascinating platform of sharing knowledge and interests. The emergence of various social networks has greatly enriched our daily life, and simultaneously, it brings a challenging task to identify influencers among multiple social networks. The key problem lies in the various interactions among individuals and huge data scale. Aiming at solving the problem, this paper employs a general multilayer network model to represent the multiple social networks, and then proposes the node influence indicator merely based on the local neighboring information. Extensive experiments on 21 real-world datasets are conducted to verify the performance of the proposed method, which shows superiority to the competitors. It is of remarkable significance in revealing the evolutions in social networks and we hope this work will shed light for more and more forthcoming researchers to further explore the uncharted part of this promising field.<\/jats:p>","DOI":"10.3390\/e22040450","type":"journal-article","created":{"date-parts":[[2020,4,16]],"date-time":"2020-04-16T05:15:41Z","timestamp":1587014141000},"page":"450","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Identifying Influencers in Social Networks"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6446-8612","authenticated-orcid":false,"given":"Xinyu","family":"Huang","sequence":"first","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7863-1230","authenticated-orcid":false,"given":"Dongming","family":"Chen","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongqi","family":"Wang","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Ren","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep01060","article-title":"Surprise maximization reveals the community structure of complex networks","volume":"3","author":"Aldecoa","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5547","DOI":"10.1038\/srep05547","article-title":"Searching for superspreaders of information in real-world social media","volume":"4","author":"Pei","year":"2014","journal-title":"Sci. Rep."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Xu, Z., Rui, X., He, J., Wang, Z., and Hadzibeganovic, T. (2019). Superspreaders and superblockers based community evolution tracking in dynamic social networks. Knowl.-Based Syst., 105377.","DOI":"10.1016\/j.knosys.2019.105377"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"19307","DOI":"10.1038\/srep19307","article-title":"Locating influential nodes in complex networks","volume":"6","author":"Malliaros","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/j.physa.2017.12.087","article-title":"BridgeRank: A novel fast centrality measure based on local structure of the network","volume":"496","author":"Salavati","year":"2018","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_6","first-page":"1465","article-title":"Social network coalescence based on multilayer network model","volume":"20","author":"Huang","year":"2019","journal-title":"J. Nonlinear Convex Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"063108","DOI":"10.1063\/1.4985185","article-title":"Identifying key nodes in multilayer networks based on tensor decomposition","volume":"27","author":"Wang","year":"2017","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1093\/comnet\/cnu016","article-title":"Multilayer networks","volume":"2","author":"Arenas","year":"2014","journal-title":"J. Complex Netw."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2014.07.001","article-title":"The structure and dynamics of multilayer networks","volume":"544","author":"Boccaletti","year":"2014","journal-title":"Phys. Rep."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Rodrigues, F.A. (2019). Network centrality: an introduction. A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems, Springer.","DOI":"10.1007\/978-3-319-78512-7_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.jnca.2018.01.005","article-title":"Influence analysis in social networks: A survey","volume":"106","author":"Peng","year":"2018","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Grover, A., and Leskovec, J. (2016, January 13\u201317). node2vec: Scalable feature learning for networks. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939754"},{"key":"ref_13","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_14","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_15","doi-asserted-by":"crossref","first-page":"025103","DOI":"10.1103\/PhysRevE.69.025103","article-title":"Structural vulnerability of the North American power grid","volume":"69","author":"Albert","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1038\/nature10011","article-title":"Controllability of complex networks","volume":"473","author":"Liu","year":"2011","journal-title":"Nature"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"046108","DOI":"10.1103\/PhysRevE.73.046108","article-title":"Efficient routing on complex networks","volume":"73","author":"Yan","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1007\/s00500-012-0962-x","article-title":"Diversity-maintained differential evolution embedded with gradient-based local search","volume":"17","author":"Xie","year":"2013","journal-title":"Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1080\/0022250X.1972.9989806","article-title":"Factoring and weighting approaches to status scores and clique identification","volume":"2","author":"Bonacich","year":"1972","journal-title":"J. Math. Sociol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1146\/annurev.soc.27.1.415","article-title":"Birds of a feather: Homophily in social networks","volume":"27","author":"McPherson","year":"2001","journal-title":"Annu. Rev. Sociol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.socnet.2004.11.008","article-title":"Centrality and network flow","volume":"27","author":"Borgatti","year":"2005","journal-title":"Soc. Netw."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2307\/3033543","article-title":"A set of measures of centrality based on betweenness","volume":"40","author":"Freeman","year":"1977","journal-title":"Sociometry"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0378-8733(78)90021-7","article-title":"Centrality in social networks conceptual clarification","volume":"1","author":"Freeman","year":"1978","journal-title":"Soc. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1086\/228631","article-title":"Power and centrality: A family of measures","volume":"92","author":"Bonacich","year":"1987","journal-title":"Am. J. Sociol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0169-7552(98)00110-X","article-title":"The anatomy of a large-scale hypertextual web search engine","volume":"30","author":"Brin","year":"1998","journal-title":"Comput. Netw. ISDN Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3747","DOI":"10.1073\/pnas.0400087101","article-title":"The architecture of complex weighted networks","volume":"101","author":"Barrat","year":"2004","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Chen, D.B., Gao, H., L\u00fc, L., and Zhou, T. (2013). Identifying influential nodes in large-scale directed networks: The role of clustering. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0077455"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.physa.2015.12.162","article-title":"Identifying influential spreaders in complex networks based on gravity formula","volume":"451","author":"Ma","year":"2016","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1142\/S0219525903001067","article-title":"Community structure in jazz","volume":"6","author":"Gleiser","year":"2003","journal-title":"Adv. Complex Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"8577","DOI":"10.1073\/pnas.0601602103","article-title":"Modularity and community structure in networks","volume":"103","author":"Newman","year":"2006","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1038\/nphys560","article-title":"Reaction-diffusion processes and metapopulation models in heterogeneous networks","volume":"3","author":"Colizza","year":"2007","journal-title":"Nat. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"8387","DOI":"10.1038\/s41598-019-44930-9","article-title":"Identifying influential spreaders by gravity model","volume":"9","author":"Li","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_34","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_35","doi-asserted-by":"crossref","unstructured":"L\u00fc, L., Zhang, Y.C., Yeung, C.H., and Zhou, T. (2011). Leaders in social networks, the delicious case. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0021202"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1109\/TNSE.2016.2600059","article-title":"Information propagation in clustered multilayer networks","volume":"3","author":"Zhuang","year":"2016","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/TNSE.2017.2775152","article-title":"Identifying influential spreaders in complex multilayer networks: A centrality perspective","volume":"6","author":"Basaras","year":"2017","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_38","unstructured":"Cozzo, E., Kivel\u00e4, M., De Domenico, M., Sol\u00e9, A., Arenas, A., G\u00f3mez, S., Porter, M.A., and Moreno, Y. (2013). Clustering coefficients in multiplex networks. arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1093\/comnet\/cnx050","article-title":"Centralities of nodes and influences of layers in large multiplex networks","volume":"6","author":"Rahmede","year":"2018","journal-title":"J. Complex Netw."},{"key":"ref_40","first-page":"5","article-title":"Identifying Top-k Most Influential Nodes by using the Topological Diffusion Models in the Complex Networks","volume":"4","author":"Paidar","year":"2017","journal-title":"Network"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s41060-019-00183-3","article-title":"Resampling-based predictive simulation framework of stochastic diffusion model for identifying top-K influential nodes","volume":"9","author":"Ohara","year":"2020","journal-title":"Int. J. Data Sci. Anal."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.physa.2018.09.040","article-title":"Identification of top-k influential nodes based on enhanced discrete particle swarm optimization for influence maximization","volume":"513","author":"Tang","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Silber, M.D. (2011). The Al Qaeda Factor: Plots against the West, University of Pennsylvania Press.","DOI":"10.2307\/j.ctt3fj4zt"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1137\/S0036144500371907","article-title":"The mathematics of infectious diseases","volume":"42","author":"Hethcote","year":"2000","journal-title":"SIAM Rev."},{"key":"ref_45","unstructured":"Guan-Rong, C., Xiao-Fan, W., and Xiang, L. (2012). Introduction to Complex Networks: Models, Structures and Dynamics, Higher Education Press."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"342","DOI":"10.2307\/2393394","article-title":"Assessing the political landscape: Structure, cognition, and power in organizations","volume":"35","author":"Krackhardt","year":"1990","journal-title":"Adm. Sci. Q."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1086\/jar.33.4.3629752","article-title":"An information flow model for conflict and fission in small groups","volume":"33","author":"Zachary","year":"1977","journal-title":"J. Anthropol. Res."},{"key":"ref_48","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. Sociobiol."},{"key":"ref_49","unstructured":"Tsvetovat, M., and Kouznetsov, A. (2011). Social Network Analysis for Startups: Finding Connections on the Social Web, O\u0154eilly Media, Inc."},{"key":"ref_50","unstructured":"Knuth, D.E. (1993). The Stanford GraphBase: A Platform for Combinatorial Algorithms, SODA."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1038\/ng881","article-title":"Network motifs in the transcriptional regulation network of Escherichia coli","volume":"31","author":"Milo","year":"2002","journal-title":"Nat. Genet."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Rossi, R., and Ahmed, N. (2015, January 25\u201330). The network data repository with interactive graph analytics and visualization. Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, Austin, TX, USA.","DOI":"10.1609\/aaai.v29i1.9277"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"027104","DOI":"10.1103\/PhysRevE.72.027104","article-title":"Community detection in complex networks using extremal optimization","volume":"72","author":"Duch","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"W76","DOI":"10.1093\/nar\/gku367","article-title":"WormNet v3: A network-assisted hypothesis-generating server for Caenorhabditis elegans","volume":"42","author":"Cho","year":"2014","journal-title":"Nucleic Acids Res."},{"key":"ref_55","first-page":"1259","article-title":"The Rise of the Medici","volume":"98","author":"Action","year":"1993","journal-title":"Am. J. Sociol."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0378-8733(87)90009-8","article-title":"Cognitive social structures","volume":"9","author":"Krackhardt","year":"1987","journal-title":"Soc. Netw."},{"key":"ref_57","unstructured":"Vickers, M., and Chan, S. (1981). Representing Classroom Social Structure, Victoria Institute of Secondary Education."},{"key":"ref_58","unstructured":"Kapferer, B. (1972). Strategy and Transaction in an African Factory: African Workers and Indian Management in a Zambian Town, Manchester University Press."},{"key":"ref_59","unstructured":"Lazega, E. (2001). The Collegial Phenomenon: The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership, Oxford University Press on Demand."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1111\/j.1467-9531.2006.00176.x","article-title":"New specifications for exponential random graph models","volume":"36","author":"Snijders","year":"2006","journal-title":"Sociol. Methodol."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"D535","DOI":"10.1093\/nar\/gkj109","article-title":"BioGRID: a general repository for interaction datasets","volume":"34","author":"Stark","year":"2006","journal-title":"Nucleic Acids Res."},{"key":"ref_62","unstructured":"Magnani, M., Micenkova, B., and Rossi, L. (2013). Combinatorial analysis of multiple networks. arXiv."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"8351","DOI":"10.1073\/pnas.1318469111","article-title":"Navigability of interconnected networks under random failures","volume":"111","author":"Arenas","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1038\/srep01344","article-title":"Emergence of network features from multiplexity","volume":"3","author":"Cardillo","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1093\/biomet\/30.1-2.81","article-title":"A new measure of rank correlation","volume":"30","author":"Kendall","year":"1938","journal-title":"Biometrika"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/450\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:45:04Z","timestamp":1760363104000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/4\/450"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,15]]},"references-count":65,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["e22040450"],"URL":"https:\/\/doi.org\/10.3390\/e22040450","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,15]]}}}