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Y-index: An effective method to measure the importance of nodes in a directed weighted network

Published:17 November 2023Publication History

ABSTRACT

This paper proposes Y-index as the basic index of directed weighted network to measure the importance of nodes in the network. Considering the large number of nodes in most real networks, in order to improve the computing speed, we introduce the Y-index of synchronous iteration and asynchronous iteration. It is proved that the iterative Y-index sequence is convergent and converges to the same value. The experimental results of Facebook network and Adolescent health network show that, compared with other H-type index, Y-index can well measure the importance of nodes in directed weighted network, which shows that Y-index is effective.

References

  1. A. Barrat, M. Barthelemy, R. Pastor-Satorras, and A. Vespignani. 2004. The architecture of complex weighted networks. Proceedings of the National Academy of Sciences of the United States of America 101 (2004), 3747–3752.Google ScholarGoogle ScholarCross RefCross Ref
  2. Alex Bavelas. 1950. Communication patterns in task-oriented groups. Acoustical Society of America 22, 6 (1950), 725–730.Google ScholarGoogle ScholarCross RefCross Ref
  3. Phillip Bonacich. 1972. Factoring and weighting approaches to status scores and clique identification. The Journal of Mathematical Sociology 2, 1 (1972), 113–120.Google ScholarGoogle ScholarCross RefCross Ref
  4. Stephen P. Borgatti. 2005. Centrality and network flow. Social Networks 27, 1 (2005), 55–71.Google ScholarGoogle ScholarCross RefCross Ref
  5. Stephen P. Borgatti and Martin G. Everett. 2006. A graph-theoretic perspective on centrality. Social Networks 28, 4 (2006), 466–484.Google ScholarGoogle ScholarCross RefCross Ref
  6. Reuven Cohen, Keren Erez, Daniel ben Avraham, and Shlomo Havlin. 2001. Breakdown of the internet under intentional attack. Phys Rev Lett 86, 16 (2001), 3682–3685.Google ScholarGoogle ScholarCross RefCross Ref
  7. Linton C. Freeman. 1978. Centrality in social networks conceptual clarification. Social Networks 1, 3 (1978), 215–239.Google ScholarGoogle ScholarCross RefCross Ref
  8. J. E. Hirsch. 2005. An index to quantify an individual’s scientific research output. Proceedings of the National Academy of Sciences of the United States of America 102 (2005), 16569–16572.Google ScholarGoogle ScholarCross RefCross Ref
  9. M. O. Jackson. 2008. Social and economic networks. Princeton University Press.Google ScholarGoogle Scholar
  10. M. G. Kendall. 1938. A new measure of rank correlation. Biometrika 30 (1938), 81–93.Google ScholarGoogle ScholarCross RefCross Ref
  11. Maksim Kitsak, Lazaros Gallos, Shlomo Havlin, Fredrik Liljeros, Lev Muchnik, H. Stanley, and Hernan Makse. 2010. Identification of influential spreaders in complex networks. Nature Physics 6 (2010), 888–893.Google ScholarGoogle ScholarCross RefCross Ref
  12. András Korn, Andras Schubert, and András Telcs. 2009. Lobby index in networks. Physica A: Statistical Mechanics and its Applications 388 (2009), 2221–2226.Google ScholarGoogle Scholar
  13. Linyuan Lü, Duanbing Chen, Xiao-Long Ren, Qian-Ming Zhang, Yi-Cheng Zhang, and Tao Zhou. 2016. Vital nodes identification in complex networks. Physics Reports 650 (2016), 1–63.Google ScholarGoogle ScholarCross RefCross Ref
  14. Linyuan Lü, Tao Zhou, Qian-Ming Zhang, and H. Eugene Stanley. 2016. The H-index of a network node and its relation to degree and coreness. Nature Communications 7 (2016), 10168.Google ScholarGoogle ScholarCross RefCross Ref
  15. James Moody. 2001. Peer influence groups: identifying dense clusters in large networks. Social Networks 23, 4 (2001), 261–283.Google ScholarGoogle ScholarCross RefCross Ref
  16. Mark Newman. 2010. Networks: an introduction. Oxford: Oxford University Press.Google ScholarGoogle Scholar
  17. J. Nieminen. 1974. On the centrality in a graph. Scandinavian Journal of Psychology 15, 1 (1974), 332–336.Google ScholarGoogle ScholarCross RefCross Ref
  18. Tore Opsahl and Pietro Panzarasa. 2009. Clustering in weighted networks. Social Networks 31, 2 (2009), 155–163.Google ScholarGoogle ScholarCross RefCross Ref
  19. Albert Réka, Jeong Hawoong, and Barabási Albert-László. 2000. Error and attack tolerance of complex networks. Nature 406 (2000), 378–382.Google ScholarGoogle ScholarCross RefCross Ref
  20. Gert Sabidussi. 1966. The centrality index of a graph. Psychometrika 31, 4 (1966), 581–603.Google ScholarGoogle ScholarCross RefCross Ref
  21. Andras Schubert, Andras Korn, and Andras Telcs. 2009. Hirsch-type indices for characterizing networks. Scientometrics 78 (2009), 375–382.Google ScholarGoogle ScholarCross RefCross Ref
  22. Qiuyan Shang, Yong Deng, and Kang Hao Cheong. 2021. Identifying influential nodes in complex networks: effective distance gravity model. Information Sciences 577 (2021), 162–179.Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Qiuyan Shang, Bolong Zhang, Hanwen Li, and Yong Deng. 2021. Identifying influential nodes: a new method based on network efficiency of edge weight updating. Chaos: An Interdisciplinary Journal of Nonlinear Science 31, 3 (2021), 033120.Google ScholarGoogle ScholarCross RefCross Ref
  24. Duncan J. Watts and Steven H. Strogatz. 1998. Collective dynamics of ’small-world’ networks. Nature 393 (1998), 440–442.Google ScholarGoogle ScholarCross RefCross Ref
  25. Xiangbin Yan, Li Zhai, and Weiguo Fan. 2013. C-index: a weighted network node centrality measure for collaboration competence. Journal of Informetrics 7, 1 (2013), 223–239.Google ScholarGoogle ScholarCross RefCross Ref
  26. Hu Yang, Jar-Der Luo, Ying Fan, and Li Zhu. 2020. Using weighted k-means to identify chinese leading venture capital firms incorporating with centrality measures. Information Processing and Management 57, 2 (2020), 102083.Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Li Zhai, Xiangbin Yan, and Guojing Zhang. 2013. A centrality measure for communication ability in weighted network. Physica A Statistical Mechanics and its Applications 392, 23 (2013), 6107–6117.Google ScholarGoogle Scholar
  28. Li Zhai, Xiangbin Yan, and Guojing Zhang. 2018. Bi-directional h-index: a new measure of node centrality in weighted and directed networks. Journal of Informetrics 12, 1 (2018), 299–314.Google ScholarGoogle ScholarCross RefCross Ref
  29. Li Zhai, Xiangbin Yan, and Bin Zhu. 2014. The hi-index: improvement of h-index based on quality of citing papers. Scientometrics 98, 2 (2014), 1021–1031.Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Jie Zhao, Yutong Song, Fan Liu, and Yong Deng. 2021. The identification of influential nodes based on structure similarity. Connection Science 33, 2 (2021), 201–218.Google ScholarGoogle ScholarCross RefCross Ref
  31. Jie Zhao, Yunchuan Wang, and Yong Deng. 2020. Identifying influential nodes in complex networks from global perspective. Chaos, Solitons and Fractals 133 (2020), 109637.Google ScholarGoogle ScholarCross RefCross Ref
  32. Na Zhao, Jie Li, Jian Wang, Tong Li, Yong Yu, and Tao Zhou. 2020. Identifying significant edges via neighborhood information. Physica A: Statistical Mechanics and its Applications 548 (2020), 123877.Google ScholarGoogle Scholar
  33. Star Zhao, Ronald Rousseau, and Fred Ye. 2011. H-degree as a basic measure in weighted networks. Journal of Informetrics 5 (2011), 668–677.Google ScholarGoogle ScholarCross RefCross Ref
  34. Star X. Zhao and Fred Y. Ye. 2012. Exploring the directed h-degree in directed weighted networks. Journal of Informetrics 6, 4 (2012), 619–630.Google ScholarGoogle ScholarCross RefCross Ref

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          • Published in

            cover image ACM Other conferences
            ADMIT '23: Proceedings of the 2023 2nd International Conference on Algorithms, Data Mining, and Information Technology
            September 2023
            227 pages
            ISBN:9798400707629
            DOI:10.1145/3625403

            Copyright © 2023 ACM

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            Publication History

            • Published: 17 November 2023

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