{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:25:47Z","timestamp":1767705947216,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T00:00:00Z","timestamp":1557446400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61841701"],"award-info":[{"award-number":["61841701"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Due to the growing interconnections of social networks, the problem of influence maximization has been extended from a single social network to multiple social networks. However, a critical challenge of influence maximization in multi-social networks is that some initial seed nodes may be unable to be active, which obviously leads to a low performance of influence spreading. Therefore, finding substitute nodes for mitigating the influence loss of uncooperative nodes is extremely helpful in influence maximization. In this paper, we propose three substitute mining algorithms for influence maximization in multi-social networks, namely for the Greedy-based substitute mining algorithm, pre-selected-based substitute mining algorithm, and similar-users-based substitute mining algorithm. The simulation results demonstrate that the existence of the uncooperative seed nodes leads to the range reduction of information influence. Furthermore, the viability and performance of the proposed algorithms are presented, which show that three substitute node mining algorithms can find suitable substitute nodes for multi-social networks influence maximization, thus achieves better influence.<\/jats:p>","DOI":"10.3390\/fi11050112","type":"journal-article","created":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T03:57:07Z","timestamp":1557719827000},"page":"112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Substitute Seed Nodes Mining Algorithms for Influence Maximization in Multi-Social Networks"],"prefix":"10.3390","volume":"11","author":[{"given":"Xuli","family":"Rao","sequence":"first","affiliation":[{"name":"Department of Computer Science, Fuzhou Polytechnic, Fuzhou 350108, Fujian, China"},{"name":"College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350007, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4302-3531","authenticated-orcid":false,"given":"Jiaxu","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Fuzhou Polytechnic, Fuzhou 350108, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhide","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350007, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Fuzhou Polytechnic, Fuzhou 350108, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,10]]},"reference":[{"key":"ref_1","first-page":"219","article-title":"Social Network Analysis Methods and Applications","volume":"91","author":"Wasserman","year":"1995","journal-title":"Contemp. Sociol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhan, Q., Zhang, J., and Philip, S.Y. (2018). Integrated anchor and social link predictions across multiple social networks. Knowl. Inf. Syst., 1\u201324.","DOI":"10.1007\/s10115-018-1210-1"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bakshy, E., Rosenn, I., Marlow, C., and Adamic, L. (2012, January 16\u201320). The role of social networks in information diffusion. Proceedings of the 21st International Conference on World Wide Web, Lyon, France.","DOI":"10.1145\/2187836.2187907"},{"key":"ref_4","first-page":"34","article-title":"Research on the Communication Dynamics Model of Social Network Public Opinion Based on the SIS Model","volume":"12","author":"Zhao","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ins.2015.01.034","article-title":"Identifying effective influencers based on trust for electronic word-of-mouth marketing","volume":"306","author":"Liu","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kempe, D., and Kleinberg, J. (2003, January 24\u201327). Maximizing the spread of influence through a social network. Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, USA.","DOI":"10.1145\/956750.956769"},{"key":"ref_7","unstructured":"Chen, W., Wang, Y., and Yang, S. (July, January 28). Efficient influence maximization in social networks. Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Paris, France."},{"key":"ref_8","first-page":"1","article-title":"Scalable Influence Maximization for Multiple Products in Continuous-Time Diffusion Networks","volume":"18","author":"Du","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/TNET.2016.2563397","article-title":"Adaptive Influence Maximization in Dynamic Social Networks","volume":"25","author":"Tong","year":"2017","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.1109\/JSYST.2014.2369526","article-title":"PPRank: Economically Selecting Initial Users for Influence Maximization in Social Networks","volume":"11","author":"Wang","year":"2017","journal-title":"IEEE Syst. J."},{"key":"ref_11","first-page":"643","article-title":"Influence maximization on multiple social network","volume":"39","author":"Li","year":"2016","journal-title":"Chin. J. Comput."},{"key":"ref_12","first-page":"1709","article-title":"Influence Maximization Acros Multi-Channels in Social Network","volume":"53","author":"Li","year":"2016","journal-title":"J. Comput. Res. Dev."},{"key":"ref_13","unstructured":"Shen, Y., Dinh, T.N., Zhang, H., and Thai, M.T. (November, January 29). Interest-matching information propagation in multiple online social networks. Proceedings of the International Conference on Information and Knowledge Management, Maui, HI, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1109\/TNET.2015.2394793","article-title":"Least cost influence maximization across multiple social networks","volume":"24","author":"Zhang","year":"2016","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Nguyen, D.T., Das, S., and Thai, M.T. (2013, January 9\u201313). Influence maximization in multiple online social networks. Proceedings of the International Conference on Global Communications Conference, Atlanta, GA, USA.","DOI":"10.1109\/GLOCOM.2013.6831541"},{"key":"ref_16","first-page":"199","article-title":"Influence maximization on multi-social networks based on bridge users","volume":"26","author":"Zhao","year":"2017","journal-title":"Comput. Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, C.T., Hsieh, H.P., Lin, S.D., and Shan, M.K. (2012, January 16\u201320). Finding influential seed successors in social networks. Proceedings of the 21st International Conference Companion on World Wide Web, Lyon, France.","DOI":"10.1145\/2187980.2188125"},{"key":"ref_18","first-page":"674","article-title":"Discovering the substitutes for the seeds in influence maximization problem","volume":"40","author":"Ma","year":"2017","journal-title":"Chin. J. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.future.2018.04.026","article-title":"A novel IT\u00d6 Algorithm for influence maximization in the large-scale social networks","volume":"88","author":"Wang","year":"2018","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., and Glance, N.S. (2007, January 12\u201315). Cost-effective outbreak detection in networks. Proceedings of the 13th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, San Jose, CA, USA.","DOI":"10.1145\/1281192.1281239"},{"key":"ref_21","unstructured":"Goyal, A., Lu, W., and Lakshmanan, L.V.S. (April, January 28). CELF++: Optimizing the greedy algorithm for influence maximization in social networks. Proceedings of the International Conference on World Wide Web, Hyderabad, India."}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/5\/112\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:50:54Z","timestamp":1760187054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/5\/112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,10]]},"references-count":21,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["fi11050112"],"URL":"https:\/\/doi.org\/10.3390\/fi11050112","relation":{},"ISSN":["1999-5903"],"issn-type":[{"type":"electronic","value":"1999-5903"}],"subject":[],"published":{"date-parts":[[2019,5,10]]}}}