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Identifying vital spreaders in complex networks based on the interpretative structure model and improved Kshell

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Abstract

The identification of vital spreaders in complex networks has been one of the most interesting topics in network science. Several methods were proposed to deal with this challenge, but there still exist deficiencies in previous methods, such as excessive time complexity, inadequate accuracy of recognition results after dividing the topological structure, and the ignorance of neighbors’ attribute information in the links’ significance model. To address these issues and promote identifying ability more effectively, the proposed extended centrality upon hybrid information, named EISMC, introduces the interpretative structure model (ISM) and improves hierarchical weight results after the division in hierarchies. Based on the hierarchical structure of Improved Kshell decomposition (IKs), the weight value of each layer is updated, and meanwhile the local centrality under link significance (LinkC) is created to supplement local features in this method. In this paper, six real-world networks and nine comparison methods are applied to conduct a series of simulations and tests. Results demonstrate that the proposed method outperforms state-of-the-art algorithms in the identifying effects for good spreading influence.

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References

  1. Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268–276

    Article  Google Scholar 

  2. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D-U (2006) Complex networks: structure and dynamics. Phys Rep 424(4–5):175–308

    Article  MathSciNet  Google Scholar 

  3. Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47

    Article  MathSciNet  Google Scholar 

  4. Song C, Havlin S, Makse HA (2005) Self-similarity of complex networks. Nature 433(7024):392–395

    Article  Google Scholar 

  5. Ruths J, Ruths D (2014) Control profiles of complex networks. Science 343(6177):1373–1376

    Article  MathSciNet  Google Scholar 

  6. Pagani GA, Aiello M (2013) The power grid as a complex network: a survey. Phys A Stat Mech Appl 392(11):2688–2700

    Article  MathSciNet  Google Scholar 

  7. Chen C, Zhou X, Li Z, He Z, Li Z, Lin X (2018) Novel complex network model and its application in identifying critical components of power grid. Phys A Stat Mech Appl 512:316–329

    Article  Google Scholar 

  8. Curado M, Tortosa L, Vicent JF, Yeghikyan G (2020) Analysis and comparison of centrality measures applied to urban networks with data. J Comput Sci 43:101127

    Article  Google Scholar 

  9. Lin J, Ban Y (2013) Complex network topology of transportation systems. Transp Rev 33(6):658–685

    Article  Google Scholar 

  10. De Bona AA, Oliveira Rosa M, Fonseca KVO, Lüders R (2021) A reduced model for complex network analysis of public transportation systems. Phys A Stat Mech Appl 567:125715

    Article  Google Scholar 

  11. Xu R, Mi C, Mierzwiak R, Meng R (2020) Complex network construction of internet finance risk. Phys A Stat Mech Appl 540:122930

    Article  Google Scholar 

  12. Fadhil SA (2021) Internet of things security threats and key technologies. J Discret Math Sci Cryptogr 24(7):1951–1957

    Article  Google Scholar 

  13. Zengler K, Zaramela LS (2018) The social network of microorganisms-how auxotrophies shape complex communities. Nat Rev Microbiol 16(6):383–390

    Article  Google Scholar 

  14. Centola D (2010) The spread of behavior in an online social network experiment. Science 329(5996):1194–1197

    Article  Google Scholar 

  15. Zhao Z, Chen D, Wang L, Han C (2018) Credit risk diffusion in supply chain finance: a complex networks perspective. Sustainability 10(12):4608

    Article  Google Scholar 

  16. Fath BD, Scharler UM, Ulanowicz RE, Hannon B (2007) Ecological network analysis: network construction. Ecol Model 208(1):49–55

    Article  Google Scholar 

  17. Hughes J, Allen RC, Baguelin M, Hampson K, Baillie GJ, Elton D, Newton JR, Kellam P, Wood JL, Holmes EC et al (2012) Transmission of equine influenza virus during an outbreak is characterized by frequent mixed infections and loose transmission bottlenecks. PLoS Pathogens 8(12):1003081

    Article  Google Scholar 

  18. Wertheim JO, Leigh Brown AJ, Hepler NL, Mehta SR, Richman DD, Smith DM, Kosakovsky Pond SL (2014) The global transmission network of HIV-1. J Infect Dis 209(2):304–313

    Article  Google Scholar 

  19. Zhong S, Zhang H, Deng Y (2022) Identification of influential nodes in complex networks: a local degree dimension approach. Inf Sci 610:994–1009

    Article  Google Scholar 

  20. Barabási A-L (2013) Network science. Philos Trans Royal Soc A Math Phys Eng Sci 371(1987):20120375

    Google Scholar 

  21. Khosravi E, Yazdanifar F, Salimi N, Beni HA (2023) Identify initial nodes for spreader in a new diffusion model based on topology (dbt) in social networks. In: 2023 9th International Conference on Web Research (ICWR), pp. 52–57. IEEE

  22. Tong T, Dong Q, Sun J, Jiang Y (2023) Vital spreaders identification synthesizing cross entropy and information entropy with kshell method. Expert Syst Appl 224:119928

    Article  Google Scholar 

  23. Liu X, Ye S, Fiumara G, De Meo P (2022) Influential spreaders identification in complex networks with topsis and k-shell decomposition. IEEE Trans Comput Soc Syst 10(1):347–361

    Article  Google Scholar 

  24. Bonacich P (1972) Factoring and weighting approaches to status scores and clique identification. J Math Sociol 2(1):113–120

    Article  Google Scholar 

  25. Li Z, Ren T, Ma X, Liu S, Zhang Y, Zhou T (2019) Identifying influential spreaders by gravity model. Sci Rep 9(1):1–7

    Google Scholar 

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

    Article  Google Scholar 

  27. Yang X-H, Xiong Z, Ma F, Chen X, Ruan Z, Jiang P, Xu X (2021) Identifying influential spreaders in complex networks based on network embedding and node local centrality. Phys A Stat Mech Appl 573:125971

    Article  Google Scholar 

  28. Xu G-Q, Meng L, Tu D-Q, Yang P-L (2021) Lch: A local clustering h-index centrality measure for identifying and ranking influential nodes in complex networks. Chin Phys B 30(8):088901

    Article  Google Scholar 

  29. Wen T, Pelusi D, Deng Y (2020) Vital spreaders identification in complex networks with multi-local dimension. Knowl Based Syst 195:105717

    Article  Google Scholar 

  30. 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  Google Scholar 

  31. Liu Z, Jiang C, Wang J, Yu H (2015) The node importance in actual complex networks based on a multi-attribute ranking method. Knowl Based Syst 84:56–66

    Article  Google Scholar 

  32. Ma L-L, Ma C, Zhang H-F, Wang B-H (2016) Identifying influential spreaders in complex networks based on gravity formula. Phys A Stat Mech Appl 451:205–212

    Article  Google Scholar 

  33. Liu J-G, Ren Z-M, Guo Q (2013) Ranking the spreading influence in complex networks. Phys A Stat Mech Appl 392(18):4154–4159

    Article  Google Scholar 

  34. Liu Y, Tang M, Zhou T, Do Y (2015) Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition. Sci Rep 5(1):1–8

    Google Scholar 

  35. Sun PG, Miao Q, Staab S (2021) Community-based k-shell decomposition for identifying influential spreaders. Pattern Recogn 120:108130

    Article  Google Scholar 

  36. Bao Z-K, Liu J-G, Zhang H-F (2017) Identifying multiple influential spreaders by a heuristic clustering algorithm. Phys Lett A 381(11):976–983

    Article  Google Scholar 

  37. Li S, Xiao F (2021) The identification of crucial spreaders in complex networks by effective gravity model. Inf Sci 578:725–749

    Article  MathSciNet  Google Scholar 

  38. Namtirtha A, Dutta A, Dutta B, Sundararajan A, Simmhan Y (2021) Best influential spreaders identification using network global structural properties. Sci Rep 11(1):1–15

    Article  Google Scholar 

  39. Wang M, Li W, Guo Y, Peng X, Li Y (2020) Identifying influential spreaders in complex networks based on improved k-shell method. Phys A Stat Mech Appl 554:124229

    Article  Google Scholar 

  40. Wan Y-P, Wang J, Zhang D-G, Dong H-Y, Ren Q-H (2018) Ranking the spreading capability of nodes in complex networks based on link significance. Phys A Stat Mech Appl 503:929–937

    Article  Google Scholar 

  41. Sun S, Ren T, Xu Y (2023) Edge-weights-based method to identify influential spreaders in complex networks. Trans Inst Meas Control, 01423312231182468

  42. Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1(3):215–239

    Article  Google Scholar 

  43. Bonacich P, Lloyd P (2001) Eigenvector-like measures of centrality for asymmetric relations. Soc Netw 23(3):191–201

    Article  Google Scholar 

  44. Bae J, Kim S (2014) Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Phys A Stat Mech Appl 395:549–559

    Article  MathSciNet  Google Scholar 

  45. Zeng A, Zhang C-J (2013) Ranking spreaders by decomposing complex networks. Phys Lett A 377(14):1031–1035

    Article  Google Scholar 

  46. Chen D, Lü L, Shang M-S, Zhang Y-C, Zhou T (2012) Identifying influential nodes in complex networks. Phys A Stat Mech Appl 391(4):1777–1787

    Article  Google Scholar 

  47. Sheikhahmadi A, Nematbakhsh MA (2017) Identification of multi-spreader users in social networks for viral marketing. J Inf Sci 43(3):412–423

    Article  Google Scholar 

  48. Mandal A, Deshmukh S (1994) Vendor selection using interpretive structural modelling (ism). Int J Oper Prod Manag

  49. Haraldsdottir S, Gupta S, Anderson RM (1992) Preliminary studies of sexual networks in a male homosexual community in Iceland. J Acq Immune Defic Syndr 5(4):374–381

    Google Scholar 

  50. Gleiser PM, Danon L (2003) Community structure in jazz. Adv Complex Syst 6(04):565–573

    Article  Google Scholar 

  51. Guimera R, Danon L, Diaz-Guilera A, Giralt F, Arenas A (2003) Self-similar community structure in a network of human interactions. Phys Rev E 68(6):065103

    Article  Google Scholar 

  52. Rozemberczki B, Allen C, Sarkar R (2021) Multi-scale attributed node embedding. J Complex Netw 9(2):014

    MathSciNet  Google Scholar 

  53. Castellano C, Pastor-Satorras R (2010) Thresholds for epidemic spreading in networks. Phys Rev Lett 105(21):218701

    Article  Google Scholar 

  54. Rezaei AA, Jalili M, Khayyam H (2021) Influential node ranking in complex networks using a randomized dynamics sensitive approach. arXiv e-prints

  55. Allen LJ (1994) Some discrete-time si, sir, and sis epidemic models. Math Biosci 124(1):83–105

    Article  Google Scholar 

  56. Zar JH (2005) Spearman rank correlation. Encycl Biostat. 7

  57. Arndt S, Turvey C, Andreasen NC (1999) Correlating and predicting psychiatric symptom ratings: Spearmans r versus kendalls tau correlation. J Psych Res 33(2):97–104

    Article  Google Scholar 

Download references

Funding

This work was supported by National Natural Science Foundation of China (Grant number: 52177090); Postgraduate Research & Practice Innovation Program of Jiangsu Province of China (Grant number: KYCX23_0476).

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, 200 Xiaolingwei, Nanjing, 210094, Jiangsu Province, China

    Tianchi Tong, Qian Dong, Wenying Yuan & Jinsheng Sun

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  1. Tianchi Tong
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Correspondence to Jinsheng Sun.

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The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: TianChi Tong reports financial support was provided by National Natural Science Foundation of China and Postgraduate Research & Practice Innovation Program of Jiangsu Province of China.

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Appendix

Appendix

Table 7 shows results of Kendall’s coefficient generated by each method and SIS in different networks in Sect. 4.4. Figure 8 represents running time costs of Cnc+, Kshell, MCDE, MDD, SCL and EISMC in six networks in Sect. 4.6.

Table 7 The correlation of different measures compared with the spreading ability is measured by Kendall’s coefficient
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Fig. 8
figure 8

Time costs of execution of different methods in six networks

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Tong, T., Dong, Q., Yuan, W. et al. Identifying vital spreaders in complex networks based on the interpretative structure model and improved Kshell. Computing (2024). https://doi.org/10.1007/s00607-024-01268-z

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