Abstract
Influence maximization problem is to select a set of influential nodes and maximize the influence spread of the seed set in the social networks. Greedy strategies are high time consumption, especially in large-scale networks, and therefore cannot be efficiently applied to practical scenarios. Meta-heuristic algorithms have been demonstrated by simulations as efficient ways to solve the intractable problem, but some of them suffer from premature easily. To solve the problem effectively, an improved discrete particle swarm optimization called IDPSO is proposed in this study. According to the framework, in the local search operation, nodes in the candidate seed set are randomly selected to be improved, giving each node an even opportunity to be selected as a candidate. Then, particles tend to be trapped into local optimum are labeled for further exploitation. Finally, local search operation is performed on the labeled particles and the current global optimal particle. Results on practical social networks show that IDPSO outperforms as a more promising and robust method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
Biswas TK, Abbasi A, Chakrabortty RK (2022) A two-stage vikor assisted multi-operator differential evolution approach for influence maximization in social networks. Exp Syst Appl 192(116):342. https://doi.org/10.1016/j.eswa.2021.116342
Bond RM, Fariss CJ, Jones JJ et al (2012) A 61-million-person experiment in social influence and political mobilization. Nature 489(7415):295–298. https://doi.org/10.1038/nature11421
Bovet A, Makse HA (2019) Influence of fake news in twitter during the 2016 us presidential election. Nat Commun 10(1):1–14. https://doi.org/10.1038/s41467-018-07761-2
Chen W, Wang Y, Yang S (2009) Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 199–208. https://doi.org/10.1145/1557019.1557047
Contractor NS, DeChurch LA (2014) Integrating social networks and human social motives to achieve social influence at scale. Proc Natl Acad Sci 111:13650–13657. https://doi.org/10.1073/pnas.1401211111
Cui L, Hu H, Yu S et al (2018) Ddse: a novel evolutionary algorithm based on degree-descending search strategy for influence maximization in social networks. J Netw Comput Appl 103:119–130. https://doi.org/10.1016/j.jnca.2017.12.003
Domingos P, Richardson M (2001) Mining the network value of customers. In: Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining, pp 57–66. https://doi.org/10.1145/502512.502525
Dong C, Xu G, Yang P et al (2023) Tsifim: a three-stage iterative framework for influence maximization in complex networks. Exp Syst Appl 212(118):702. https://doi.org/10.1016/j.eswa.2022.118702
Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1(3):215–239
Galstyan A, Musoyan V, Cohen P (2009) Maximizing influence propagation in networks with community structure. Phys Rev E 79(5):056–102. https://doi.org/10.1103/PhysRevE.79.056102
Gong M, Yan J, Shen B et al (2016) Influence maximization in social networks based on discrete particle swarm optimization. Inf Sci 367:600–614. https://doi.org/10.1016/j.ins.2016.07.012
Goyal A, Lu W, Lakshmanan LV (2011) Celf++ optimizing the greedy algorithm for influence maximization in social networks. In: Proceedings of the 20th international conference companion on World wide web, pp 47–48. https://doi.org/10.1145/1963192.1963217
Guille A, Hacid H, Favre C et al (2013) Information diffusion in online social networks: a survey. ACM Sigmod Rec 42(2):17–28. https://doi.org/10.1145/2503792.2503797
Heidari M, Asadpour M, Faili H (2015) Smg: fast scalable greedy algorithm for influence maximization in social networks. Phys A Stat Mech Appl 420:124–133. https://doi.org/10.1016/j.physa.2014.10.088
Huang H, Shen H, Meng Z et al (2019) Community-based influence maximization for viral marketing. Appl Intel 49(6):2137–2150. https://doi.org/10.1007/s10489-018-1387-8
Jiang Q, Song G, Gao C et al (2011) Simulated annealing based influence maximization in social networks. Twenty-fifth AAAI Conf Artif Intell. https://doi.org/10.1609/aaai.v25i1.7838
Kazemzadeh F, Safaei AA, Mirzarezaee M et al (2023) Determination of influential nodes based on the communities’ structure to maximize influence in social networks. Neurocomputing 534:18–28. https://doi.org/10.1016/j.neucom.2023.02.059
Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence through a social network. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pp 137–146. https://doi.org/10.1145/956750.956769
Kennedy J, Eberhart R (1995) Particle swarm optimization. pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
Kianian S, Rostamnia M (2020) An efficient path-based approach for influence maximization in social networks. Exp Syst Appl 167(6):114–168. https://doi.org/10.1016/j.eswa.2020.114168
Kitsak M, Gallos LK, Havlin S et al (2010) Identification of influential spreaders in complex networks. Nat Phys 6(11):888–893. https://doi.org/10.1038/nphys1746
Kumar S, Panda A (2021) Identifying influential nodes in weighted complex networks using an improved wvoterank approach. Appl Intel 52(2):1838–1852. https://doi.org/10.1007/s10489-021-02403-5
Kumar S, Gupta A, Khatri I (2022) Csr: a community based spreaders ranking algorithm for influence maximization in social networks. World Wide Web 25(6):2303–2322. https://doi.org/10.1007/s11280-021-00996-y
Kundu S, Murthy C, Pal SK (2011) A new centrality measure for influence maximization in social networks. In: International conference on pattern recognition and machine intelligence, pp 242–247. https://doi.org/10.1007/978-3-642-21786-9_40
Leskovec J, Krause A, Guestrin C, et al (2007) Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 420–429. https://doi.org/10.1145/1281192.1281239
Li Y, Ma S, Zhang Y et al (2013) An improved mix framework for opinion leader identification in online learning communities. Knowledge-Based Syst 43:43–51. https://doi.org/10.1016/j.knosys.2013.01.005
Li W, Zhong K, Wang J et al (2021) A dynamic algorithm based on cohesive entropy for influence maximization in social networks. Exp Syst Appl 169(114):207. https://doi.org/10.1016/j.eswa.2020.114207
Li H, Zhang R, Zhao Z et al (2021) Identification of top-k influential nodes based on discrete crow search algorithm optimization for influence maximization. Appl Intel 51:7749–7765. https://doi.org/10.1007/s10489-021-02283-9
Li W, Hu Y, Jiang C et al (2023) Abem: an adaptive agent-based evolutionary approach for influence maximization in dynamic social networks. Appl Soft Comput 136(110):062. https://doi.org/10.1016/j.asoc.2023.110062
Linyuan L, Chen D, Ren XL et al (2016) Vital nodes identification in complex networks. Phys Rep 650:1–63. https://doi.org/10.1016/j.physrep.2016.06.007
Ll Ma, Ma C, Zhang HF et al (2016) Identifying influential spreaders in complex networks based on gravity formula. Phys A Stat Mech Appl 451:205–212. https://doi.org/10.1016/j.physa.2015.12.162
Lozano-Osorio I, Sanchez-Oro J, Duarte A et al (2023) A quick grasp-based method for influence maximization in social networks. J. Ambient Intell Human Comput 14(4):3767–3779. https://doi.org/10.1007/s12652-021-03510-4
Newman ME (2005) A measure of betweenness centrality based on random walks. Soc Netw 27(1):39–54. https://doi.org/10.1016/j.socnet.2004.11.009
Pei S, Muchnik L, Andrade JS Jr et al (2014) Searching for superspreaders of information in real-world social media. Sci Rep 4(1):1–12. https://doi.org/10.1038/srep05547
Rui X, Meng F, Wang Z et al (2019) A reversed node ranking approach for influence maximization in social networks. Appl Intel 49(7):2684–2698. https://doi.org/10.1007/s10489-018-01398-w
Samir AM, Rady S, Gharib TF (2021) Lkg: A fast scalable community-based approach for influence maximization problem in social networks. Phys A Stat Mech Appl 582(126):258. https://doi.org/10.1016/j.physa.2021.126258
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence (Cat. No. 98TH8360), pp 69–73. https://doi.org/10.1109/ICEC.1998.699146
Sun PG, Miao Q, Staab S (2021) Community-based k-shell decomposition for identifying influential spreaders. Patt Recogn 120(108):130. https://doi.org/10.1016/j.patcog.2021.108130
Tang J, Zhang R, Yao Y et al (2018) Maximizing the spread of influence via the collective intelligence of discrete bat algorithm. Knowledge-Based Syst 160:88–103. https://doi.org/10.1016/j.knosys.2018.06.013
Tang J, Zhang R, Wang P et al (2020) A discrete shuffled frog-leaping algorithm to identify influential nodes for influence maximization in social networks. Knowledge-Based Syst 187(104):833. https://doi.org/10.1016/j.knosys.2019.07.004
Wang Y, Dong W, Dong X (2018) A novel itö algorithm for influence maximization in the large-scale social networks. Fut Gene Comput Syst 88:755–763. https://doi.org/10.1016/j.future.2018.04.026
Wang L, Ma L, Wang C et al (2021) Identifying influential spreaders in social networks through discrete moth-flame optimization. IEEE Trans Evolut Comput 25(6):1091–1102. https://doi.org/10.1109/TEVC.2021.3081478
Wang Y, Zheng Y, Shi X et al (2022) An effective heuristic clustering algorithm for mining multiple critical nodes in complex networks. Phys A Stat Mech Appl 588(126):535. https://doi.org/10.1016/j.physa.2021.126535
Wang Y, Cong G, Song G, et al (2010) Community-based greedy algorithm for mining top-k influential nodes in mobile social networks. In: Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 1039–1048. https://doi.org/10.1145/1835804.1835935
Xie M, Zhan XX, Liu C et al (2023) An efficient adaptive degree-based heuristic algorithm for influence maximization in hypergraphs. Inf Process Manag 60(2):103–161. https://doi.org/10.1016/j.ipm.2022.103161
Yang PL, Xu GQ, Yu Q et al (2020) An adaptive heuristic clustering algorithm for influence maximization in complex networks. Chaos Interdiscipl J Nonlinear Sci 30(19):93–106
Zareie A, Sheikhahmadi A (2018) A hierarchical approach for influential node ranking in complex social networks. Exp Syst Appl 93:200–211. https://doi.org/10.1016/j.eswa.2017.10.018
Zhang J, Chen D, Dong Q et al (2016) Identifying a set of influential spreaders in complex networks. Sci Rep 6(27):823. https://doi.org/10.1038/srep27823
Zhang S, Zeng X, Tang B (2021) Rcelf: a residual-based approach for influence maximization problem. Inf Syst 102(101):828. https://doi.org/10.1016/j.is.2021.101828
Zhu T, Wang B, Wu B et al (2014) Maximizing the spread of influence ranking in social networks. Inf Sci 278:535–544. https://doi.org/10.1016/j.ins.2014.03.070
Acknowledgements
This work was financially supported by the Zhejiang Provincial Natural Science Foundation under Grant number LQ20F020011, the National Natural Science Foundations of China under Grant number 62162040 and the National Key Research and Development Plan under Grant number 2020YFB1713600.
Funding
This work was not supported by any organization.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this article.
Ethical approval
This article does not contain any studies with animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tang, J., Zhu, H., Lan, J. et al. Identifying influential nodes for influence maximization problem in social networks using an improved discrete particle swarm optimization. Soc. Netw. Anal. Min. 13, 94 (2023). https://doi.org/10.1007/s13278-023-01098-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13278-023-01098-5