Skip to main content

An Efficient Estimation of a Node’s Betweenness

  • Conference paper

Part of the Studies in Computational Intelligence book series (SCI,volume 597)

Abstract

Betweenness Centrality measures, erstwhile popular amongst the sociologists and psychologists, have seen wide and increasing applications across several disciplines of late. In conjunction with the big data problems, there came the need to analyze large complex networks. Exact computation of a node’s betweenness is a daunting task in the networks of large size. In this paper, we propose a non-uniform sampling method to estimate the betweenness of a node. We apply our approach to estimate a node’s betweenness in several synthetic and real world graphs. We compare our method with the available techniques in the literature and show that our method fares several times better than the currently known techniques. We further show that the accuracy of our algorithm gets better with the increase in size and density of the network.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-16112-9_11
  • Chapter length: 11 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   89.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-16112-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   119.99
Price excludes VAT (USA)
Hardcover Book
USD   169.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anthonisse, J.M.: The rush in a directed graph. Stichting Mathematisch Centrum. Mathematische Besliskunde (BN 9/71), 1–10 (1971)

    Google Scholar 

  2. Bader, D.A., Kintali, S., Madduri, K., Mihail, M.: Approximating betweenness centrality. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, pp. 124–137. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  3. Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    CrossRef  MathSciNet  Google Scholar 

  4. Batagelj, V., Mrvar, A.: Pajek datasets (2006), http://vlado.fmf.uni-lj.si/pub/networks/data

  5. Brandes, U.: A faster algorithm for betweenness centrality. The Journal of Mathematical Sociology 25(2), 163–177 (2001)

    CrossRef  MATH  Google Scholar 

  6. Brandes, U., Erlebach, T. (eds.): Network Analysis. LNCS, vol. 3418. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  7. Brandes, U., Pich, C.: Centrality estimation in large networks. International Journal of Bifurcation and Chaos 17(07), 2303–2318 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. Bu, D., Zhao, Y., Cai, L., Xue, H., Zhu, X., Lu, H., Zhang, J., Sun, S., Ling, L., Zhang, N., et al.: Topological structure analysis of the protein–protein interaction network in budding yeast. Nucleic Acids Research 31(9), 2443–2450 (2003)

    CrossRef  Google Scholar 

  9. Chehreghani, M.H.: An efficient algorithm for approximate betweenness centrality computation. The Computer Journal, page bxu003 (2014)

    Google Scholar 

  10. Davis, T.A., Hu, Y.: The university of florida sparse matrix collection. ACM Transactions on Mathematical Software (TOMS) 38(1), 1 (2011)

    MathSciNet  Google Scholar 

  11. Erdos, P., Renyi, A.: On random graphs i. Publ. Math. Debrecen 6, 290–297 (1959)

    MathSciNet  Google Scholar 

  12. Freeman, L.C.: A set of measures of centrality based on betweenness. Sociometry 40(1), 35–41 (1977)

    CrossRef  Google Scholar 

  13. Geisberger, R., Sanders, P., Schultes, D.: Better Approximation of Betweenness Centrality, ch. 8, pp. 90–100 (2008)

    Google Scholar 

  14. Gkorou, D., Pouwelse, J., Epema, D., Kielmann, T., van Kreveld, M., Niessen, W.: Efficient approximate computation of betweenness centrality. In: 16th Annual Conf. of the Advanced School for Computing and Imaging, ASCI 2010 (2010)

    Google Scholar 

  15. Goel, K., Singh, R.R., Iyengar, S., Sukrit: A faster algorithm to update betweenness centrality after node alteration. In: Bonato, A., Mitzenmacher, M., Prałat, P. (eds.) WAW 2013. LNCS, vol. 8305, pp. 170–184. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  16. Green, O., McColl, R., Bader, D.A.: A fast algorithm for streaming betweenness centrality. In: 2012 International Conference on Privacy, Security, Risk and Trust (PASSAT) and 2012 International Confernece on Social Computing (SocialCom), pp. 11–20 (September 2012)

    Google Scholar 

  17. Kas, M., Wachs, M., Carley, K.M., Carley, L.R.: Incremental algorithm for updating betweenness centrality in dynamically growing networks. In: Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2013, pp. 33–40. ACM, New York (2013)

    CrossRef  Google Scholar 

  18. Kintali, S.: Betweenness centrality: Algorithms and lower bounds. arXiv preprint arXiv:0809.1906 (2008)

    Google Scholar 

  19. Knuth, D.E.: The Stanford GraphBase: a platform for combinatorial computing, vol. 37. Addison-Wesley, Reading (1993)

    Google Scholar 

  20. Lee, M.-J., Lee, J., Park, J.Y., Choi, R.H., Chung, C.-W.: Qube: A quick algorithm for updating betweenness centrality. In: Proceedings of the 21st International Conference on World Wide Web, WWW 2012, pp. 351–360. ACM, New York (2012)

    Google Scholar 

  21. Leskovec, J.: Stanford large network dataset collection (2010)

    Google Scholar 

  22. Nasre, M., Pontecorvi, M., Ramachandran, V.: Betweenness centality–incremental and faster. arXiv preprint arXiv:1311.2147 (2013)

    Google Scholar 

  23. Newman, M.: Networks: An Introduction. Oxford University Press, Inc., New York (2010)

    CrossRef  Google Scholar 

  24. Riondato, M., Kornaropoulos, E.M.: Fast approximation of betweenness centrality through sampling. In: Proceedings of the 7th ACM International Conference on Web Search and Data Mining, pp. 413–422. ACM (2014)

    Google Scholar 

  25. Sariyüce, A.E., Saule, E., Kaya, K., Çatalyürek, Ü.V.: Shattering and compressing networks for betweenness centrality. In: SIAM Data Mining Conference (SDM). SIAM (2013)

    Google Scholar 

  26. Taylor, P.J.: World city network: a global urban analysis. Psychology Press (2004)

    Google Scholar 

  27. Ulanowicz, R.E., DeAngelis, D.L.: Network analysis of trophic dynamics in south florida ecosystems. In: FY97: The Florida Bay Ecosystem, pp. 20688–20038 (1998)

    Google Scholar 

  28. Van Der Hofstad, R.: Random graphs and complex networks (2009), http://www.win.tue.nl/rhofstad/NotesRGCN.pdf

  29. Wang, X.: Deciding on the type of the degree distribution of a graph (network) from traceroute-like measurements (2011)

    Google Scholar 

  30. Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manas Agarwal .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Agarwal, M., Singh, R.R., Chaudhary, S., Iyengar, S.R.S. (2015). An Efficient Estimation of a Node’s Betweenness. In: Mangioni, G., Simini, F., Uzzo, S., Wang, D. (eds) Complex Networks VI. Studies in Computational Intelligence, vol 597. Springer, Cham. https://doi.org/10.1007/978-3-319-16112-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16112-9_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16111-2

  • Online ISBN: 978-3-319-16112-9

  • eBook Packages: EngineeringEngineering (R0)