IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0022557.html
   My bibliography  Save this article

Fast Computing Betweenness Centrality with Virtual Nodes on Large Sparse Networks

Author

Listed:
  • Jing Yang
  • Yingwu Chen

Abstract

Betweenness centrality is an essential index for analysis of complex networks. However, the calculation of betweenness centrality is quite time-consuming and the fastest known algorithm uses time and space for weighted networks, where and are the number of nodes and edges in the network, respectively. By inserting virtual nodes into the weighted edges and transforming the shortest path problem into a breadth-first search (BFS) problem, we propose an algorithm that can compute the betweenness centrality in time for integer-weighted networks, where is the average weight of edges and is the average degree in the network. Considerable time can be saved with the proposed algorithm when , indicating that it is suitable for lightly weighted large sparse networks. A similar concept of virtual node transformation can be used to calculate other shortest path based indices such as closeness centrality, graph centrality, stress centrality, and so on. Numerical simulations on various randomly generated networks reveal that it is feasible to use the proposed algorithm in large network analysis.

Suggested Citation

  • Jing Yang & Yingwu Chen, 2011. "Fast Computing Betweenness Centrality with Virtual Nodes on Large Sparse Networks," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-5, July.
    • Handle: RePEc:plo:pone00:0022557
    DOI: 10.1371/journal.pone.0022557
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0022557
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0022557&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0022557?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    4. Pietro Panzarasa & Tore Opsahl & Kathleen M. Carley, 2009. "Patterns and dynamics of users' behavior and interaction: Network analysis of an online community," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 60(5), pages 911-932, May.
    5. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
    6. Fredrik Liljeros & Christofer R. Edling & Luís A. Nunes Amaral & H. Eugene Stanley & Yvonne Åberg, 2001. "The web of human sexual contacts," Nature, Nature, vol. 411(6840), pages 907-908, June.
    7. Albert-László Barabási, 2005. "The origin of bursts and heavy tails in human dynamics," Nature, Nature, vol. 435(7039), pages 207-211, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yan, Li & Cao, Huiying & Gao, Chao & Wang, Zhen & Li, Xuelong, 2023. "Mining of book-loan behavior based on coupling relationship analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
    2. Abbasi, Alireza & Hossain, Liaquat & Leydesdorff, Loet, 2012. "Betweenness centrality as a driver of preferential attachment in the evolution of research collaboration networks," Journal of Informetrics, Elsevier, vol. 6(3), pages 403-412.
    3. Perc, Matjaž, 2010. "Growth and structure of Slovenia’s scientific collaboration network," Journal of Informetrics, Elsevier, vol. 4(4), pages 475-482.
    4. Kibae Kim & Jörn Altmann, 2015. "Effect of Homophily on Network Formation," TEMEP Discussion Papers 2015121, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Mar 2017.
    5. Michael Boss & Helmut Elsinger & Martin Summer & Stefan Thurner, 2004. "Network topology of the interbank market," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 677-684.
    6. Pi, Xiaochen & Tang, Longkun & Chen, Xiangzhong, 2021. "A directed weighted scale-free network model with an adaptive evolution mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    7. Blagus, Neli & Šubelj, Lovro & Bajec, Marko, 2012. "Self-similar scaling of density in complex real-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2794-2802.
    8. Elias Carroni & Paolo Pin & Simone Righi, 2020. "Bring a Friend! Privately or Publicly?," Management Science, INFORMS, vol. 66(5), pages 2269-2290, May.
    9. Biggiero, Lucio & Angelini, Pier Paolo, 2015. "Hunting scale-free properties in R&D collaboration networks: Self-organization, power-law and policy issues in the European aerospace research area," Technological Forecasting and Social Change, Elsevier, vol. 94(C), pages 21-43.
    10. Wu, Tao & Xian, Xingping & Zhong, Linfeng & Xiong, Xi & Stanley, H. Eugene, 2018. "Power iteration ranking via hybrid diffusion for vital nodes identification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 802-815.
    11. Xia, Ling-Ling & Song, Yu-Rong & Li, Chan-Chan & Jiang, Guo-Ping, 2018. "Improved targeted immunization strategies based on two rounds of selection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 540-547.
    12. Biao Xiong & Bixin Li & Rong Fan & Qingzhong Zhou & Wu Li, 2017. "Modeling and Simulation for Effectiveness Evaluation of Dynamic Discrete Military Supply Chain Networks," Complexity, Hindawi, vol. 2017, pages 1-9, October.
    13. He, Xuan & Zhao, Hai & Cai, Wei & Li, Guang-Guang & Pei, Fan-Dong, 2015. "Analyzing the structure of earthquake network by k-core decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 34-43.
    14. Zhengzheng Pan, 2012. "Opinions and Networks: How Do They Effect Each Other," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 157-171, February.
    15. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    16. Greg Morrison & L Mahadevan, 2012. "Discovering Communities through Friendship," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    17. Selen Onel & Abe Zeid & Sagar Kamarthi, 2011. "The structure and analysis of nanotechnology co-author and citation networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 119-138, October.
    18. Wu, Yali & Dong, Ang & Ren, Yuanguang & Jiang, Qiaoyong, 2023. "Identify influential nodes in complex networks: A k-orders entropy-based method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    19. Saban, Daniela & Bonomo, Flavia & Stier-Moses, Nicolás E., 2010. "Analysis and models of bilateral investment treaties using a social networks approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3661-3673.
    20. Erjia Yan & Ying Ding & Qinghua Zhu, 2010. "Mapping library and information science in China: a coauthorship network analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 83(1), pages 115-131, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0022557. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.