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Time-sensitive propagation values discount centrality measure

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Abstract

The detection of influential individuals in social networks is called influence maximization which has many applications in advertising and marketing. Several factors including propagation delay affect the degree to which an individual influences the network. Many different methods, including centrality measures, identify high-influence individuals in social networks. The time-sensitive harmonic method (TSHarmonic), which considers time sensitivity to propagation delay and duration, is a centrality measure. TSHarmonic has two weaknesses: high computational complexity and ignoring the influence of the selected node in selecting other influential nodes. Therefore, in this article, the valuable path-finding process in the TSHarmonic method is modified to provide the Fast Time-Sensitive Harmonic algorithm. The provided method has the same accuracy as the TSHarmonic, while the speed is significantly increased. Then, the Time-Sensitive Propagation Values Discount method is proposed to improve detection speed and accuracy. This method takes into account the influence of the selected node for future selection and hence increases the accuracy.

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References

  1. Wang M, Wang C, Yu JX, Zhang J (2015) Community detection in social networks: an in-depth benchmarking study with a procedure-oriented framework. Proc VLDB Endow 8(10):998–1009

    Article  Google Scholar 

  2. Guellil I, Boukhalfa K (2015) Social big data mining: A survey focused on opinion mining and sentiments analysis. In: 2015 12th international symposium on programming and systems (ISPS), pp 1–10. IEEE

  3. Kim TY, Kim HJ et al. (2022) Opinion mining-based term extraction sentiment classification modeling. Mobile Inf Syst 2022

  4. Yang Y, Lichtenwalter RN, Chawla NV (2015) Evaluating link prediction methods. Knowl Inf Syst 45(751–782):15

    Google Scholar 

  5. Patel R, Guo Y, Alhudhaif A, Alenezi F, Althubiti SA, Polat K et al. (2021) Graph-based link prediction between human phenotypes and genes. Math Probl Eng 2022

  6. Sun G, Chen C-C (2021) Influence maximization algorithm based on reverse reachable set. Math Probl Eng 2021:1–12

    Google Scholar 

  7. Chen J, Wei N, Yang H et al. (2022) Immune algorithm to suppress rumor propagation based on influence maximization. Secur Commun Netw 2022

  8. Wang W, Street WN (2018) Modeling and maximizing influence diffusion in social networks for viral marketing. Appl Netw Sci 3(1):1–26

    Article  ADS  Google Scholar 

  9. Domingos P, Richardson M (2002) Mining the network value of customers/proceedings of the seventh international conference on knowledge discovery and data mining. In: Proceedings of the seventh ACM SIGKDD international conference on knowledge discovery and data mining

  10. 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

  11. Zareie A, Sheikhahmadi A, Jalili M (2019) Identification of influential users in social networks based on users’ interest. Inf Sci 493:217–231

    Article  MathSciNet  Google Scholar 

  12. Li Y, Fan J, Wang Y, Tan K-L (2018) Influence maximization on social graphs: a survey. IEEE Trans Knowl Data Eng 30(10):1852–1872

    Article  Google Scholar 

  13. Peng S, Zhou Y, Cao L, Yu S, Niu J, Jia W (2018) Influence analysis in social networks: a survey. J Netw Comput Appl 106:17–32

    Article  Google Scholar 

  14. Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen J, Glance N (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

  15. 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 (2011)

  16. Wang Y, Cong G, Song G, Xie K (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

  17. Sheikhahmadi A, Nematbakhsh MA, Zareie A (2017) Identification of influential users by neighbors in online social networks. Physica A 486:517–534

    Article  ADS  Google Scholar 

  18. Chen W, Castillo C, Lakshmanan LV (2022) Information and influence propagation in social networks. Springer

  19. Galhotra S, Arora A, Roy S (2016) Holistic influence maximization: combining scalability and efficiency with opinion-aware models. In: Proceedings of the 2016 international conference on management of data, pp 743–758

  20. Jung K, Heo W, Chen W (2012) Irie: scalable and robust influence maximization in social networks. In: 2012 IEEE 12th international conference on data mining, pp 918–923. IEEE

  21. Chen W, Yuan Y, Zhang L (2010) Scalable influence maximization in social networks under the linear threshold model. In: 2010 IEEE international conference on data mining, pp 88–97. IEEE

  22. Zareie A, Sheikhahmadi A, Khamforoosh K (2018) Influence maximization in social networks based on topsis. Expert Syst Appl 108:96–107

    Article  Google Scholar 

  23. 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, pp 1029–1038

  24. Goyal A, Lu W, Lakshmanan LV (2011) Simpath: an efficient algorithm for influence maximization under the linear threshold model. In: 2011 IEEE 11th international conference on data mining, pp 211–220 (2011). IEEE

  25. Kimura M, Saito K (2006) Approximate solutions for the influence maximization problem in a social network. In: International conference on knowledge-based and intelligent information and engineering systems, pp 937–944. Springer

  26. Ohsaka N, Akiba T, Yoshida Y, Kawarabayashi K-i (2014) Fast and accurate influence maximization on large networks with pruned monte-carlo simulations. In: Proceedings of the AAAI conference on artificial intelligence

  27. Borgs C, Brautbar M, Chayes J, Lucier B (2014) Maximizing social influence in nearly optimal time. In: Proceedings of the twenty-fifth annual ACM-SIAM symposium on discrete algorithms, pp 946–957. SIAM

  28. 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 17 509–518

  29. Tang Y, Xiao X, Shi Y (2014) Influence maximization: near-optimal time complexity meets practical efficiency. In: Proceedings of the 2014 ACM SIGMOD international conference on management of data, pp 75–86

  30. Kim J, Lee W, Yu H (2014) Ct-ic: continuously activated and time-restricted independent cascade model for viral marketing. Knowl-Based Syst 62:57–68

    Article  Google Scholar 

  31. Yan R, Li Y, Li D, Zhu Y, Wang Y, Du H (2019) Activation probability maximization for target users under influence decay model. In: Computing and combinatorics: 25th international conference, COCOON 2019, Xi’an, China, 2019, Proceedings 25, pp 603–614 (2019). Springer

  32. Hu M, Liu Q, Huang H, Jia X (2018) Time-sensitive influence maximization in social networks. In: 2018 IEEE 18th international conference on communication technology (ICCT), pp 1351–1356 (2018). IEEE

  33. Wang Y, Zhang Y, Yang F, Li D, Sun X, Ma J (2021) Time-sensitive positive influence maximization in signed social networks. Physica A 584:126353

    Article  Google Scholar 

  34. Min H, Cao J, Yuan T, Liu B (2020) Topic based time-sensitive influence maximization in online social networks. World Wide Web 23:1831–1859

    Article  Google Scholar 

  35. Banerjee S, Jenamani M, Pratihar DK (2022) An approximate marginal spread computation approach for the budgeted influence maximization with delay. Computing 104(3):657–680

    Article  MathSciNet  Google Scholar 

  36. Goyal A, Bonchi F, Lakshmanan LV (2010) Learning influence probabilities in social networks. In: Proceedings of the third ACM international conference on web search and data mining, pp 241–250

  37. Saito K, Kimura M, Ohara K, Motoda H (2009) Learning continuous-time information diffusion model for social behavioral data analysis. In: Advances in machine learning: first Asian conference on machine learning, ACML 2009, Nanjing, China, November 2–4, 2009. Proceedings 1, pp 322–337. Springer

  38. Lotf JJ, Azgomi MA, Dishabi MRE (2022) An improved influence maximization method for social networks based on genetic algorithm. Physica A 586:126480

    Article  Google Scholar 

  39. Wan Z, Mahajan Y, Kang BW, Moore TJ, Cho J-H (2021) A survey on centrality metrics and their network resilience analysis. IEEE Access 9(104773–104819):18

    Google Scholar 

  40. Freeman LC et al (2002) Centrality in social networks: conceptual clarification. Soc Netw Crit Concepts Sociol 1:238–263

    Google Scholar 

  41. 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

  42. Wang X, Su Y, Zhao C, Yi D (2016) Effective identification of multiple influential spreaders by degree punishment. Physica A 461:238–247

    Article  ADS  Google Scholar 

  43. Jia P, Liu J, Huang C, Liu L, Xu C (2019) An improvement method for degree and its extending centralities in directed networks. Physica A 532:121891

    Article  Google Scholar 

  44. Joyce KE, Laurienti PJ, Burdette JH, Hayasaka S (2010) A new measure of centrality for brain networks. PLoS ONE 5(8):12200

    Article  ADS  Google Scholar 

  45. Raychaudhuri A, Mallick S, Sircar A, Singh S (2020) Identifying influential nodes based on network topology: a comparative study. In: Information, photonics and communication: proceedings of second national conference, IPC 2019, pp 65–76. Springer

  46. Keskin ME, G¨uler MG, (2018) Influence maximization in social networks: an integer programming approach. Turkish J Electr Eng Comput Sci 26(6):3383–3396

    Google Scholar 

  47. Kundu S, Murthy C, Pal SK (2011) A new centrality measure for influence maximization in social networks. In: Pattern recognition and machine intelligence: 4th International Conference, PReMI 2011, Moscow, Russia, 2011. Proceedings 4, pp 242–247 (2011). Springer

  48. Bonacich P (2007) Some unique properties of eigenvector centrality. Soc Netw 29(4):555–564

    Article  Google Scholar 

  49. Kitsak M, Gallos LK, Havlin S, Liljeros F, Muchnik L, Stanley HE, Makse HA (2010) Identification of influential spreaders in complex networks. Nat Phys 6(11):888–893

    Article  CAS  Google Scholar 

  50. Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1):39–43

    Article  Google Scholar 

  51. Bae J, Kim S (2014) Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A 395(549–559):19

    MathSciNet  Google Scholar 

  52. Brin S, Page L (1998) The anatomy of a large-scale hypertextual web search engine. Comput Netw ISDN Syst 30(1–7):107–117

    Article  Google Scholar 

  53. Chatterjee B, Bhattacharyya T, Ghosh KK, Chatterjee A, Sarkar R (2023) A novel meta-heuristic approach for influence maximization in social networks. Expert Syst 40(4):12676

    Article  Google Scholar 

  54. Kumar S, Lohia D, Pratap D, Krishna A, Panda B (2022) Mder: modified degree with exclusion ratio algorithm for influence maximisation in social networks. Computing 104(2):359–382

    Article  MathSciNet  Google Scholar 

  55. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry, 35–41

  56. Yoshida Y (2014) Almost linear-time algorithms for adaptive betweenness centrality using hypergraph sketches. In: Proceedings of the 20th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1416–1425

  57. Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177

    Article  Google Scholar 

  58. Crescenzi P, d’Angelo G, Severini L, Velaj Y (2015) Greedily improving our own centrality in a network. In: International symposium on experimental algorithms, pp 43–55 (2015). Springer

  59. Stephenson K, Zelen M (1989) Rethinking centrality: methods and examples. Soc Netw 11(1):1–37

    Article  MathSciNet  Google Scholar 

  60. Liu Y, Tang M, Zhou T, Do Y (2016) Identify influential spreaders in complex networks, the role of neighborhood. Physica A 452:289–298

    Article  ADS  Google Scholar 

  61. Shimbel A (1953) Structural parameters of communication networks. Bull Math Biophys 15:501–507

    Article  MathSciNet  Google Scholar 

  62. Alhajj R, Rokne J (2014) Encyclopedia of social network analysis and mining. Springer

  63. Mohammadi A, Saraee M, Mirzaei A (2015) Time-sensitive influence maximization in social networks. J Inf Sci 41(6):765–778

    Article  Google Scholar 

  64. Mokhtarizadeh S, Zamani Dehkordi B, Mosleh M, Barati A (2021) Influence maximization using time delay based harmonic centrality in social networks. Tabriz J Electr Eng 51(3):359–370

    Google Scholar 

  65. Adineh M, Nouri-Baygi M (2019) High quality degree based heuristics for the influence maximization problem. arXiv preprint arXiv:1904.12164 20

  66. Saxena A, Iyengar S (2020) Centrality measures in complex networks: a survey. arXiv preprint arXiv:2011.07190

  67. Hanauer K, Schulz C, Trummer J (2022) O’reach: even faster reachability in large graphs. ACM J Exp Algorithmics 27:1–27

    MathSciNet  Google Scholar 

  68. Pettie S (2004) A new approach to all-pairs shortest paths on real-weighted graphs. Theoret Comput Sci 312(1):47–74

    Article  MathSciNet  Google Scholar 

  69. Saha A, Sengupta N, Ramanath M (2019) Reachability in large graphs using bloom filters. In: 2019 IEEE 35th international conference on data engineering workshops (ICDEW), pp 217–224 (2019). IEEE

  70. Cormen TH, Leiserson CE, Rivest RL, Stein C (2013) Introduction to algorithms second edition. the knuth-morris-pratt algorithm, 2001. On quantitative evaluation of systems, qest. In: Proceedings, vol 8054, pp 22–38

  71. Thorup M (2004) Compact oracles for reachability and approximate distances in planar digraphs. J ACM (JACM) 51(6):993–1024

    Article  MathSciNet  Google Scholar 

  72. Kameda T (1975) On the vector representation of the reachability in planar directed graphs. Inf Process Lett 3(3):75–77

    Article  MathSciNet  Google Scholar 

  73. Jin R, Ruan N, Xiang Y, Wang H (2011) Path-tree: an efficient reachability indexing scheme for large directed graphs. ACM Transact Database Syst (TODS) 36(1):1–44

    Article  CAS  Google Scholar 

  74. Kunegis J (2013) Konect: the koblenz network collection. In: Proceedings of the 22nd international conference on world wide web, pp 1343–1350

  75. Leskovec J, Huttenlocher D, Kleinberg J (2010) Signed networks in social media. In: Proceedings of the SIGCHI conference on human factors in computing systems, pp 1361–1370

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Acknowledgements

The author is deeply thankful to the editor and reviewers for their valuable suggestions to improve the quality and presentation of the paper.

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Correspondence to Behzad Zamani Dehkordi.

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Mokhtarzadeh, S., Zamani Dehkordi, B., Mosleh, M. et al. Time-sensitive propagation values discount centrality measure. Computing (2024). https://doi.org/10.1007/s00607-024-01265-2

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