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Influence maximization (IM) in complex networks with limited visibility using statistical methods

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Abstract

This article delves into the analysis and identification of influential individuals within social networks, a fundamental issue in the realm of social network science and complex network analysis. Within social networks, the impact of individuals on information propagation, sha** beliefs, and influencing the behavior of others is of paramount importance. Most of the current methods are based on the assumption that the entire graph is visible. However, this assumption does not hold for many real-world graphs. This study is conducted to extend current maximization methods, with link prediction techniques to pseudo-visibility graphs. The proposed method in this paper leverages graph models and influence algorithms to identify and select influential individuals within a social network. It begins by employing graph models to predict connections within the network and subsequently employs influence algorithms to opt for the most suitable individuals for exerting influence within the network. The primary advantage of this approach lies in its capability to enhance communication and influence within social networks with minimal observation. This method aids in a better understanding of the network's structure and the behaviors of its members, ultimately facilitating more effective information dissemination. In this study, we implemented five concepts for influence maximization in the context of the proposed method. Our results indicate that the algorithms perform best when considering lower diffusion coefficients. This suggests that focusing on lower diffusion coefficients allows the algorithm to demonstrate its superiority. Additionally, our findings reveal a notable consistency in results across various graph removal scenarios, highlighting a key advantage of our proposed approach on real-world graphs.

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Data Availability

A significant amount of data and codes are addressed in this article. The data were provided from the Snap dataset of Stanford University, which is freely available to the public at http://snap.stanford.edu. The codes provided by the authors of these studies, which were in C +  + language, were used in the implementations. All implementations are available at https://github.com/sdghafouri/IMinPO. The authors declare that all the experimental data and codes in this paper are true, valid and available. Moreover, The authors declare that all experimental data are obtained from detailed experiments.

References

  1. Kempe D, Kleinberg J, Tardos E (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

  2. Zhao Y, Wu YJ, Levina E, Zhu J (2017) Link prediction for partially observed networks. J Comput Graph Stat 26(3):725–733

    MathSciNet  Google Scholar 

  3. Zhang C, Zhai BY, Wu M (2023) Link prediction of community in microblog based on exponential random graph model. In: 16th International Symposium on Wireless Personal Multimedia Communications (WPMC), Atlantic City, NJ, USA

  4. Shojaie A (2013) Link prediction in biological networks using multi-mode exponential random graph models. In: Eleventh Workshop on Mining and Learning with Graphs. Chicago, Illinois, USA, pp 971–978

  5. Burt RS (1992) Structural holes: the social structure of competition. Harvard University Press, Cambridge, p 313

    Google Scholar 

  6. Fisher ML, Nemhauser GL, Wolsey LA (1978) An analysis of approximations for maximizing submodular set functions—II, Polyhedral Combinatorics, pp 73–87

  7. Peng B (2021) Dynamic influence maximization. In: 35th Conference on Neural Information Processing Systems

  8. Jung K, Heo W, Chen W (2012) IRIE: scalable and robust influence maximization in social networks. In: IEEE 12th International Conference on Data Mining, pp 918–923

  9. Cheng S, Shen H, Huang J, Chen W, Cheng X (2014) IMRank: influence maximization via finding self-consistent ranking. In: Proceedings of the 37th International ACM SIGIR Conference on Research & Development in Information Retrieval, pp 475–484

  10. Cheng S, Shen H, Huang J, Zhang G, Cheng X (2013) StaticGreedy: solving the scalability-accuracy dilemma in influence maximization. In: Proceedings of the 22nd ACM International Conference on Information & Knowledge Management, pp 509–518

  11. Jabari Lotfi J, Abdollahi Azgomi M, Ebrahimi Dishabi MR (2022) An improved influence maximization method for social networks based on genetic algorithm, ELSEVIER. Phys A Stat Mech Appl 586

  12. Zhang S, Huang Y, Sun J, Lin W, **ao X, Tang B (2023) Capacity constrained influence maximization in social networks, The technical report in SIGKDD'23, Long Beach, CA, USA

  13. Yuxin Y, Chen Y, Han W (2022) Influence maximization in social networks: theories, methods and challenges, ELSEVIER, Array, vol 6

  14. Zareie A, Sakellariou R (2023) Influence maximization in social networks: a survey of behaviour-aware methods. Springer, Berlin

    Google Scholar 

  15. Goyal A, Lu W, Lakshmanan LVS (2011) SIMPATH: an efficient algorithm for influence maximization under the linear threshold model. In: IEEE 11th International Conference on Data Mining, Vancouver, BC, Canada, pp 211–220

  16. Kumar S, Singhla L, **dal K, Grover K (2021) IM-ELPR: influence maximization in social networks using label propagation based community structure. Appl Intell 51:4–5

    Google Scholar 

  17. Galhotra S, Arora A, Virinchi S, Roy S (2015) ASIM: a scalable algorithm for influence maximization under the independent cascade model. In: Proceedings of the 24th International Conference on World Wide Web, Florence, Italy, pp 35–36

  18. Rezvanian A, Vahidipour SM, Meybodi MR (2023) A new stochastic diffusion model for influence maximization in social networks. Sci Rep 13:67–75

    Google Scholar 

  19. Wang Q, ** Y, Lin Z, Cheng S, Yang T (2016) Influence maximization in social networks under an independent cascade-based model. Physica A 444:20–34

    ADS  MathSciNet  Google Scholar 

  20. Goyal A, Lu W, Lakshmanan LVS (2011) CELF++: optimizing the greedy algorithm for influence maximization in social networks. In: Proceedings of the 20th International Conference Companion on World Wide Web, Hyderabad, India, pp 47–48

  21. Chen W, Wang C, Wang Y (2010) Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, USA, pp 1029–1038

  22. 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, Paris, France, pp 199–208

  23. Kimura M, Saito K (2006) Tractable models for information diffusion in social networks. Eur Conf Princ Data Mini Knowl Dis 4213:259–271

    Google Scholar 

  24. Hao F, Chen M, Zhu C, Guizani M (2012) Discovering influential users in micro-blog marketing with influence maximization mechanism. In: IEEE Global Communications Conference (GLOBECOM), Anaheim, CA, USA, pp 470–474

  25. He Q, Wang X, Huang M, Lv J, Ma L (2018) Heuristics-based influence maximization for opinion formation in social networks. Appl Soft Comput 66:360–369

    Google Scholar 

  26. Stein S, Eshghi S, Maghsudi S, Tassiulas L, Bellamy RKE, Jennings NR (2017) Heuristic algorithms for influence maximization in partially observable social networks. In: Proceedings of the 3rd International Workshop on Social Influence Analysis, Melbourne, Australia

  27. Yang L, Tian Y, Li J, Ma J, Zhang J (2017) Identifying opinion leaders in social networks with topic limitation. Clust Comput 20(3):2403–2413

    Google Scholar 

  28. Wang Z, Du C, Fan J, **ng Y (2017) Ranking influential nodes in social networks based on node position and neighborhood. Neurocomputing 260:466–477

    Google Scholar 

  29. Alp ZZ, Oguducu SG (2018) Identifying topical influencers on twitter based on user behavior and network topology. Knowl-Based Syst 141:211–221

    Google Scholar 

  30. de Andrade RL, Rego LC (2018) The use of nodes attributes in social network analysis with an application to an international trade network. Physica A 491:249–270

    ADS  MathSciNet  Google Scholar 

  31. Ahajjam S, El Haddad M, Badir H (2018) A new scalable leader-community detection approach for community detection in social networks. Soc Netw 54:41–49

    Google Scholar 

  32. Azcorra A, Chiroque LF, Cuevas R, Anta AF, Laniado H, Lillo RE, Romo J, Sguera C (2018) Unsupervised scalable statistical method for identifying influential users in online social networks. Sci Rep 8:6955

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  33. Zareie A, Sheikhahmadi A, Jalili M (2019) Influential node ranking in social networks based on neighborhood diversity. Fut Gener Comput Syst 94:120–129

    Google Scholar 

  34. Wang S, Cuomo S, Mei G, Cheng W, Xu N (2019) Efficient method for identifying influential vertices in dynamic networks using the strategy of local detection and updating. Futur Gener Comput Syst 91:10–24

    Google Scholar 

  35. Kumar S, Panda BS (2020) Identifying influential nodes in social networks: neighborhood coreness based voting approach. Physica A Stat Mech Appl 553:52238

    Google Scholar 

  36. Berahmand K, Bouyer A, Samadi N (2018) A new centrality measure based on the negative and positive effects of clustering coefficient for identifying influential spreaders in complex networks. Chaos Solitons Fractals 110:41–54

    ADS  Google Scholar 

  37. Zareie A, Sheikhahmadi A, Jalili M, Fasaei MSK (2020) Finding influential nodes in social networks based on neighborhood correlation coefficient. Knowl-Based Syst 194:528

    Google Scholar 

  38. Berahmand K, Bouyer A, Samadi N (2019) A new local and multidimensional ranking measure to detect spreaders in social networks. Computing 110:1711–1733

    MathSciNet  Google Scholar 

  39. Debnath S, Sarkar D, Jana P (2020) Top-k influential nodes identification based on activity behaviors in egocentric online social networks. Comput Intell Pattern Recogn 5:463–475

    Google Scholar 

  40. Kermani MAMA, Aliahmadi A, Hanneman R (2016) Optimizing the choice of influential nodes for diffusion on a social network. Int J Commun Syst 29(7):1235–1250

    Google Scholar 

  41. Song G, Li Y, Chen X, He X, Tang J (2017) Influential node tracking on dynamic social network: an interchange greedy approach. IEEE Trans Knowl Data Eng 29(2):359–372

    ADS  Google Scholar 

  42. More JS, Lingam C (2019) A gradient-based methodology for optimizing time for influence diffusion in social networks. Soc Netw Anal Mini 9:5

    Google Scholar 

  43. Liqing Q, Chunmei G, Shuang Z, **angbo T, Mingjv Z (2020) TSIM: a two-stage selection algorithm for influence maximization in social networks. IEEE Access 8:12084–12095

    Google Scholar 

  44. Zhang Z, Li X, Gan C (2021) Identifying influential nodes in social networks via community structure and influence distribution difference. Dig Commun Netw 7:131–139

    Google Scholar 

  45. Ullah A, Wang B, Sheng J, Long J, Khan N (2021) Identification of influential nodes via effective distance-based centrality mechanism in complex networks. Complexity 5:1–16

    Google Scholar 

  46. Berahmand K, Samadi N, Sheikholeslami SM (2018) Effect of rich-club on diffusion in complex networks. Int J Modern Phys B 32:12

    Google Scholar 

  47. Wang B, Zhang J, Dai J, Sheng J (1833) Influential nodes identification using network local structural properties. Sci Rep 12(1):2022

    Google Scholar 

  48. Mukhtar MF, Abas ZA, Rasib AHA, Anuar SHH, Zaki NHM, Rahman AFNA, Abidin ZZ, Shibghatullah AS (2022) Identifying influential nodes with centrality indices combinations using symbolic regression. Int J Adv Comput Sci Appl 13(5):592–599

    Google Scholar 

  49. Budak C, Agrawal D, El Abbadi A (2011) Limiting the spread of misinformation in social networks. In: Proceedings of the 20th International Conference on World Wide Web, pp 665–674, Hyderabad, India

  50. He X, Song G, Chen W, Jiang Q (2012) Influence blocking maximization in social networks under the competitive linear threshold model. In: Proceedings of the 2012 SIAM International Conference on Data Mining, Society for Industrial and Applied Mathematics, pp 463–474

  51. Fan L, Lu Z, Wu W, Thuraisingham B, Ma H, Bi Y (2013) Least cost rumor blocking in social networks. In: IEEE 33rd International Conference on Distributed Computing Systems, pp 540–549, Philadelphia, PA, USA

  52. Zhao Y, Li S, ** F (2016) Identification of influential nodes in social networks with community structure based on label propagation. Neurocomputing 210:34–44

    Google Scholar 

  53. Wang B, Chen G, Fu L, Song L, Wang X (2017) DRIMUX: dynamic rumor influence minimization with user experience in social networks. IEEE Trans Knowl Data Eng 29(10):2168–2181

    Google Scholar 

  54. Wu P, Pan L (2017) Scalable influence blocking maximization in social networks under competitive independent cascade models. Comput Netw 123:38–50

    Google Scholar 

  55. Yang W, Brenner L, Giua A (2018) Influence maximization by link activation in social networks. In: IEEE 23rd International Conference on Emerging Technologies and Factory Automation (ETFA), Turin, Italy

  56. Fischetti M, Kahr M, Leitner M, Monaci M, Ruthmair M (2018) Least cost influence propagation in (Social) networks. Math Program 170(1):293–325

    MathSciNet  Google Scholar 

  57. Bucur D, Iacca G, Marcelli A, Squillero G, Tonda A (2018) Improving multi-objective evolutionary influence maximization in social networks. In: International Conference on the Applications of Evolutionary Computation, pp 117–124

  58. Li CT, Lin YJ, Yeh MY (2018) Forecasting participants of information diffusion on social networks with its applications. Inf Sci 422:432–446

    Google Scholar 

  59. Gulati A, Eirinaki M (2018) Influence propagation for social graph-based recommendations. In: IEEE International Conference on Big Data, Seattle, WA, USA, pp 2180–2189

  60. **e G, Chen Y, Zhang H, Liu Y (2019) MBIC: a novel influence propagation model for membership-based influence maximization in social networks. IEEE Access 7:75696–75707

    Google Scholar 

  61. Chen Y, Qu Q, Ying Y, Li H, Shen J (2020) Semantics-aware influence maximization in social networks. Inf Sci 513:442–464

    MathSciNet  Google Scholar 

  62. Rui X, Yang X, Fan J, Wang Z (2020) A neighbour scale fixed approach for influence maximization in social networks. Computing 106(6):427–449

    MathSciNet  Google Scholar 

  63. Wu Q, Zhou L, Huang Y (2020) Influence maximization based on community closeness in social networks. In: Web Information Systems Engineering, Singapore, pp 142–156

  64. Amiri B, Fathian M, Asaadi E (2021) Influence maximization in complex social networks based on community structure. J Ind Syst Eng 13(3):16–40

    Google Scholar 

  65. Wang W, Yang H, Lu Y, Zou Y, Zhang X, Guo S, Lin L (2021) Influence maximization in multi-relational social networks. In: 30th ACM International Conference on Information and Knowledge Management

  66. Lotf JJ, Azgomi MA, Dishabi MRE (2022) An improved influence maximization method for social networks based on genetic algorithm. Physica A Stat Mech Appl 586:528

    Google Scholar 

  67. S. Kummar, A. Mallik, A. Khetarpal, B.S. panda, "Influence maximization in social networks using graph embedding and graph neural network", Information Sciences, 2022.

  68. Kumar S, Mallik A, Panda BS (2023) Influence maximization in social networks using transfer learning via graph-based LSTM. Expert Syst Appl 212:5236

    Google Scholar 

  69. Frank O, Strauss D (1986) Markov graphs. J Am Stat Assoc 81(395):832–842

    MathSciNet  Google Scholar 

  70. Robins G, Pattison P, Kalish Y, Lusher D (2007) An introduction to exponential random graph (p*) models for social networks. Soc Netw 29(2):173–191

    Google Scholar 

  71. Snijders TAB, Pattison PE, Robins GL, Handcock MS (2006) New specifications for exponential random graph models. Sociol Methodol 36(1):99–152

    Google Scholar 

  72. Lusher D, Koskinen J, Robins G (2012) Exponential random graph models for social networks: theory, methods, and applications. Cambridge University Press, Cambridge

    Google Scholar 

  73. Ghafouri S, Khasteh SH (2019) Influence maximization under partially observable environments. In: IEEE 27th Iranian Conference on Electrical Engineering, Yazd, Iran

  74. Hagberg A, Chult DS, Swart P (2008) Exploring network structure, dynamics, and function using networkX. In: 7th Python in Science Conference

  75. Handcock MS, Hunter DR, Butts CT, Goodreau SM, Morris M (2008) Statnet: software tools for the representation, visualization, analysis and simulation of network data. J Stat Softw 24(1):1548

    PubMed  PubMed Central  Google Scholar 

  76. Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans Knowl Discov Data 1(1):1–41

    Google Scholar 

  77. Stewart J, Schweinberger M, Bojanowski M, Morris M (2019) Multilevel network data facilitate statistical inference for curved ERGMs with geometrically weighted terms. Soc Netw 59:98–119

    Google Scholar 

  78. Saxena R, Jadeja M, Vyas P (2023) An efficient influence maximization technique based on betweenness centrality measure and clustering coefficient (Bet-Clus). In: 15th International Conference on Computer and Automation Engineering, Sydney, Australia

  79. Hosseini-Pozveh M, Shahreza ML (2023) A new PageRank-based method for influence maximization in signed social networks. J Comput Secur 10(1):61–74

    Google Scholar 

  80. Ou J, Buskens V, Rijt AVD, Panja D (2022) Influence maximization under limited network information: seeding high-degree neighbors. J Phys Complex 3:4

    Google Scholar 

  81. Bojchevski A, Shchur O, Zügner D, Günnemann S (2018) NetGAN: generating graphs via random walks. In: 35th International Conference on Machine Learning, Stockholm, Sweden, pp 609–618

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  1. K.N. Toosi University of Technology, Tehran, Iran

    Saeid Ghafouri, Seyed Hossein Khasteh & Seyed Omid Azarkasb

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  1. Saeid Ghafouri
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SG, SHK and SOA. These authors contributed equally to this work.

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Correspondence to Seyed Omid Azarkasb.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. This article does not contain any studies with animals performed by any of the authors.

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Ghafouri, S., Khasteh, S.H. & Azarkasb, S.O. Influence maximization (IM) in complex networks with limited visibility using statistical methods. J Supercomput 80, 6809–6854 (2024). https://doi.org/10.1007/s11227-023-05695-1

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