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Escape velocity centrality: escape influence-based key nodes identification in complex networks

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Abstract

Evaluating and measuring key nodes in highly populated networks is essential to control the spreading effects of diseases or rumors. Although several incentive approaches have been proposed in complex networks to identify key nodes, these approaches still have many challenges. Most of the existing approaches consider just a single aspect of a node in a network. To cope with these challenges, based on the escape velocity formula, we propose Escape Velocity Centrality (EVC) approach to combine the concerned features of the network (i.e., local and global features) to measure key nodes in complex networks with spreading dynamics. Furthermore, we design an extended version of EVC (i.e., EVC+) to enhance the overall performance. To evaluate the effectiveness of EVC & EVC+, we implemented the proposed model via real-world as well as artificial networks. The empirical results based on susceptible–infected–recovered (SIR) and Kendall's correlation evaluation modelshave demonstrated that EVC & EVC+ outperformed the state-of-the-art centralities with remarkable margins of improvements with respect to all of the facets of evaluation.

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References

  1. Li H, Zhang R, Zhao Z, Liu X, Yuan Y (2021) Identification of top-k influential nodes based on discrete crow search algorithm optimization for influence maximization. Appl Intell:1–17

  2. Mnasri W, Azaouzi M, Romdhane LB (2021) Parallel social behavior-based algorithm for identification of influential users in social network. Appl Intell:1–19

  3. Bahadori S, Moradi P, Zare H (2021) An improved limited random walk approach for identification of overlapping communities in complex networks. Appl Intell 51:3561–3580

    Article  Google Scholar 

  4. Qiu L, Zhang J, Tian X (2021) Ranking influential nodes in complex networks based on local and global structures. Appl Intell:1–14

  5. Tidke B, Mehta R, Dhanani J (2020) Consensus-based aggregation for identification and ranking of top-k influential nodes. Neural Comput Appl 32:10275–10301

    Article  Google Scholar 

  6. Li D, Wang X, Huang P (2017) A fractal growth model: exploring the connection pattern of hubs in complex networks. Physica A: Stat Mech its Appl 471:200–211 URL https://www.sciencedirect.com/science/article/pii/S0378437116310184

    Article  Google Scholar 

  7. Zhao J-H, Zeng D-L, Qin J-T, Si H-M, Liu X-F (2021) Simulation and modeling of microblog-based spread of public opinions on emergencies. Neural Comput Applic 33:547–564

    Article  Google Scholar 

  8. Parastvand H, Chapman A, Bass O, Lachowicz S (2021) Graph automorphic approaches to the robustness of complex networks. Control Eng Pract 108:104705

    Article  Google Scholar 

  9. Ren T et al (2020) Identifying vital nodes based on reverse greedy method. Sci Rep 10:1–8

    Google Scholar 

  10. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D (2006) Complex networks: Struct Dynam Phys reports. 424

  11. Yan Y, Qian Y, Sharif H, Tipper D (2012) A survey on smart grid communication infrastructures: motivations, requirements and challenges. IEEE Commun Surv Tutor 15:5–20

    Article  Google Scholar 

  12. Faloutsos, M., Faloutsos, P. & Faloutsos, C. On power-law relationships of the internet topology. In The Structure and Dynamics of Networks, 195–206 Princeton University Press, (2011)

  13. Kai-Quan C, Jun Z, Wen-Bo D, Xian-Bin C (2012) Analysis of the chinese air route network as a complex network. Chin Physics B 21:028903

    Article  Google Scholar 

  14. Garlaschelli D, Caldarelli G, Pietronero L (2003) Universal scaling relations in food webs. Nature 423:165–168

    Article  MATH  Google Scholar 

  15. Cui Y, Wang X, Li J (2014) Detecting overlapping communities in networks using the maximal sub-graph and the clustering coefficient. Physica A: Stat Mech Appl, URL 405:85–91 https://www.sciencedirect.com/science/article/pii/S0378437114002222

  16. Milo R, Itzkovitz S, Kashtan N, Chklovskii D, Shen-Orr S, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298:824

    Article  Google Scholar 

  17. Amancio D et al (2011) Using metrics from complex networks to evaluate machine translation. Physica A: Stat Mech Appl 390:131–142

    Article  MathSciNet  Google Scholar 

  18. Sheng J et al (2019) Community detection based on human social behavior. Physica A: Stat Mech Appl 531:121765

    Article  Google Scholar 

  19. Estrada, E. Introduction to complex networks: structure and dynamics. In Evolutionary equations with applications in natural sciences, 93–131 Springer, (2015)

  20. Sheng J et al (2019) FluidC+: a novel community detection algorithm based on fluid propagation. Int J Modern Physics C 30.04:1950021

    Article  Google Scholar 

  21. Wang X, Zhao T, Qin X (2016) Model of epidemic control based on quarantine and message delivery. Physica A: Stat Mech Appl 458:168–178

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang X, Zhao T (2017) Model for multi-messages spreading over complex networks considering the relationship between messages. Commun Nonlinear Sci Numer Simul 48:63–69

    Article  MATH  Google Scholar 

  23. Li J, Wang X, Eustace J (2013) Detecting overlapping communities by seed community in weighted complex networks. Physica A: Stat Mech Appl 392:6125–6134

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Zhang Q, Li M, Deng Y (2018) Measure the structure similarity of nodes in complex networks based on relative entropy. Physica A: Stat Mech Appl 491:749–763

    Article  MathSciNet  MATH  Google Scholar 

  26. Wang XF (2002) Complex networks: topology, dynamics and synchronization. Int J Bifurcation Chaos 12:885–916

    Article  MathSciNet  MATH  Google Scholar 

  27. Bian T, Deng Y (2017) A new evidential methodology of identifying influential nodes in complex networks. Chaos, Solitons & Fractals 103:101–110

    Article  MathSciNet  MATH  Google Scholar 

  28. Barthelemy M (2004) Betweenness centrality in large complex networks. Eur Phys J B 38:163–168

    Article  Google Scholar 

  29. Page L, Brin S, Motwani R, Winograd T (1999) The pagerank citation ranking: bringing order to the web. Tech. Rep, Stanford InfoLab

    Google Scholar 

  30. Brin S & Page L (1998) The anatomy of a large-scale hypertextual web search engine

  31. Simsek A (2021) Lexical sorting centrality to distinguish spreading abilities of nodes in complex networks under the susceptible- infectious-recovered (sir) model. arXiv preprint arXiv:2101.10975

  32. Ibnoulouafi A, El Haziti M (2018) Density centrality: identifying influential nodes based on area density formula. Chaos, Solitons Fractals 114:69–80

    Article  MATH  Google Scholar 

  33. Zekun W, Xiangxi W, Minggong W (2019) Identification of key nodes in aircraft state network based on complex network theory. IEEE Access 7:60957–60967

    Article  Google Scholar 

  34. Liu B, Li Z, Chen X, Huang Y, Liu X (2017) Recognition and vulnerability analysis of key nodes in power grid based on complex network centrality. IEEE Trans Circ Syst II: Express Briefs 65:346–350

    Google Scholar 

  35. Tulu MM, Hou R, Younas T (2018) Identifying influential nodes based on community structure to speed up the dissemination of information in complex network. IEEE Access 6:7390–7401

    Article  Google Scholar 

  36. Wang Q et al (2018) Cda: a clustering degree based influential spreader identification algorithm in weighted complex network. IEEE Access 6:19550–19559Wang, Q.et al Cda: a clustering degree based influential spreader identification algorithm in weighted complex network. IEEE Access 6, 19550–19559 (2018)

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

    Article  Google Scholar 

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

  39. Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Networks 1:215–239

    Article  Google Scholar 

  40. Liu J, Xiong Q, Shi W, Shi X, Wang K (2016) Evaluating the importance of nodes in complex networks. Physica A: Stat Mech Appl 452:209–219

    Article  Google Scholar 

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

    Article  Google Scholar 

  42. Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E 78:046110

    Article  Google Scholar 

  43. Bian T, Deng Y (2018) Identifying influential nodes in complex networks: a node information dimension approach. Chaos: Interdiscipl J Nonlinear Sci 28:043109

    Article  MathSciNet  MATH  Google Scholar 

  44. Liu F, Wang Z, Deng Y (2020) Gmm: a generalized mechanics model for identifying the importance of nodes in complex networks. Knowl-Based Syst 193:105464

    Article  Google Scholar 

  45. Fei L, Zhang Q, Deng Y (2018) Identifying influential nodes in complex networks based on the inverse-square law. Physica A: Stat Mech Appl 512:1044–1059

    Article  Google Scholar 

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

    Article  Google Scholar 

  47. Estrada E, Rodríguez-Velázquez JA (2005) Subgraph centrality in complex networks. Phys Rev E 71:056103

    Article  MathSciNet  Google Scholar 

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

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

    Article  MATH  Google Scholar 

  50. Ullah A, Wang B, Sheng JF, Long J, Khan N, Sun ZJ (2021) Identifying vital nodes from local and global perspectives in complex networks. Expert Syst Appl 186:115778

    Article  Google Scholar 

  51. Aman U et al (2021) Identification of nodes influence based on global structure model in complex networks. Scientific Reports 11:1–11

    Google Scholar 

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

    Google Scholar 

  53. Dai J, Wang B, Sheng J, Sun Z, Khawaja FR, Ullah A, Dejene DA, Duan G (2019) Identifying influential nodes in complex networks based on local neighbor contribution. IEEE Access 7:131719–131731

    Article  Google Scholar 

  54. Zareie A, Sheikhahmadi A, Jalili M, Fasaei MSK (2020) Finding influential nodes in social networks based on neighborhood correlation coefficient. Knowledge-Based Syst:105580

  55. Zhong J, Zhang F, Li Z (2018) Identification of vital nodes in complex network via belief propagation and node reinsertion. IEEE Access 6:29200–29210

    Article  Google Scholar 

  56. Zareie A, Sheikhahmadi A, Jalili M (2020) Identification of influential users in social network using gray wolf optimization algorithm. Expert Syst Appl 142:112971

    Article  Google Scholar 

  57. Sun Z, Wang B, Sheng J, Hu Y, Wang Y, Shao J (2017) Identifying influential nodes in complex networks based on weighted formal concept analysis. IEEE Access 5:3777–3789

    Article  Google Scholar 

  58. Qiao T, Shan W, Yu G, Liu C (2018) A novel entropy-based centrality approach for identifying vital nodes in weighted networks. Entropy 20:261

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  60. Maji G, Namtirtha A, Dutta A, Malta MC (2020) Influential spreaders identification in complex networks with improved k-shell hybrid method. Expert Syst Appl 144:113092

    Article  Google Scholar 

  61. Li Z et al (2019) Identifying influential spreaders by gravity model. Sci Rep 9:1–7

    Google Scholar 

  62. Güvenc U, Katırcıoǧlu F (2019) Escape velocity: a new operator for gravitational search algorithm. Neural Comput & Applic 31:27–42

    Article  Google Scholar 

  63. Guimer R, Danon L, Daz-Guilera A, Giralt FA (2003) Arenas, Self-similar community structure in a network of human interactions. Phys. Rev. E 6:8065103

    Google Scholar 

  64. Federal Aviation Administration, Air traffic control system command center, http://www.fly.faa.gov/, (2017)

  65. Cohen W Enron email dataset, URL: http://www.cs.cmu.edu/~enron/. Accessed in (2009)

  66. SocioPatterns, Infectious contact networks,????URL: http://www. sociopatterns.org/datasets/

  67. Allen L (1994) J. some discrete-time si, sir, and sis epidemic models. Math Biosci 124:83–105

    Article  MATH  Google Scholar 

  68. Keeling MJ, Eames KT (2005) Networks and epidemic models. J R Soc Interface 2:295–307

    Article  Google Scholar 

  69. Kendall MG (1945) The treatment of ties in ranking problems. Biometrika 33:239–251

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work was supported by the National Key Research and Development Program of China under Grant no. 2018YFB1003602.

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Correspondence to Aman Ullah.

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Ullah, A., Wang, B., Sheng, J. et al. Escape velocity centrality: escape influence-based key nodes identification in complex networks. Appl Intell 52, 16586–16604 (2022). https://doi.org/10.1007/s10489-022-03262-4

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