Skip to main content
SpringerLink
Log in

A Comparison of Approaches to Computing Betweenness Centrality for Large Graphs

  • Conference paper
  • First Online:
Complex Networks & Their Applications VI (COMPLEX NETWORKS 2017)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 689))

Included in the following conference series:

Abstract

Many algorithms require doing a large number of betweenness centrality calculations quickly, and accommodating this need is an active open research area. Two of the most important ways of addressing this problem are with approximated and distributed algorithms. It is difficult to know which approach will work best in practical situations, because results presented are often compared to similar algorithms, and universally recognized benchmarks do not exist. This paper evaluates one approximation approach and one distributed approach by applying each to the problem of node-based resilience measure clustering. This form of clustering is a good test for the algorithms, because it requires massive numbers of betweenness centrality calculations, as well as results that are accurate enough for the clustering to succeed. We find that with both the approximated and distributed approaches there is a trade-off between speed and accuracy, but each succeeds in reducing computation time by at least an order of magnitude.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Available at http://www.cs.siue.edu/~gercal/clustering/.

References

  1. Arbelaitz, O., Gurrutxaga, I., Muguerza, J., PéRez, J.M., Perona, I.N.: An extensive comparative study of cluster validity indices. Pattern Recogn. 46(1), 243–256 (2013)

    Article  Google Scholar 

  2. Barefoot, C., Entringer, R., Swart, H.: Vulnerability in graphs-a comparative survey. J. Comb. Math. Comb. Comput. 1, 12–22 (1987)

    MathSciNet  MATH  Google Scholar 

  3. Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. Theory Exp. 2008(10), P10008 (2008)

    Google Scholar 

  4. Bonchi, F., De Francisci Morales, G., Riondato, M.: Centrality measures on big graphs: exact, approximated, and distributed algorithms. In: Proceedings of the 25th International Conference Companion on World Wide Web, pp. 1017–1020. International World Wide Web Conferences Steering Committee (2016)

    Google Scholar 

  5. Borwey, J., Ahlert, D., Obafemi-Ajayi, T., Ercal, G.: A graph-theoretic clustering methodology based on vertex-attack tolerance. In: The Twenty-Eighth International Flairs Conference (2015)

    Google Scholar 

  6. Brandes, U.: A faster algorithm for betweenness centrality. J. Math. Sociol. 25, 163–177 (2001)

    Article  MATH  Google Scholar 

  7. Carpenter, T., Karakostas, G., Shallcross, D.: Practical issues and algorithms for analyzing terrorist networks. In: Proceedings of the Western Simulation MultiConference (2002)

    Google Scholar 

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

    Article  Google Scholar 

  9. Chong, W.H., Toh, W.S.B., Teow, L.N.: Efficient extraction of high-betweenness vertices. In: 2010 International Conference on Advances in Social Networks Analysis and Mining (ASONAM), pp. 286–290. IEEE (2010)

    Google Scholar 

  10. Drange, P.G., Dregi, M.S., vant Hof, P.: On the computational complexity of vertex integrity and component order connectivity. In: Algorithms and Computation, pp. 285–297. Springer International Publishing (2014)

    Google Scholar 

  11. Ercal, G.: A note on the computational complexity of unsmoothened vertex attack tolerance. CoRR abs/1603.08430 (2016). http://arxiv.org/abs/1603.08430

  12. Ercal, G., Matta, J.: Resilience notions for scale-free networks. In: Complex Adaptive Systems, pp. 510–515 (2013)

    Google Scholar 

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

    Google Scholar 

  14. Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Holme, P., Kim, B.J., Yoon, C.N., Han, S.K.: Attack vulnerability of complex networks. Phys. Rev. E 65(5), 056109 (2002)

    Google Scholar 

  16. Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)

    Google Scholar 

  17. Matta, J., Obafemi-Ajayi, T., Borwey, J., Wunsch, D., Ercal, G.: Robust graph-theoretic clustering approaches using node-based resilience measures. In: 2016 IEEE 16th International Conference on Data Mining (ICDM), pp. 320–329 (2016). https://doi.org/10.1109/ICDM.2016.0043

  18. Matta, J., Ercal, G., Borwey, J.: The vertex attack tolerance of complex networks. RAIRO-Oper. Res. (2017). https://doi.org/10.1051/ro/2017008

  19. McLaughlin, A., Bader, D.A.: Scalable and high performance betweenness centrality on the gpu. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 572–583. IEEE Press (2014)

    Google Scholar 

  20. Sariyüce, A.E., Kaya, K., Saule, E., Çatalyürek, Ü.V.: Graph manipulations for fast centrality computation. ACM Trans. Knowl. Discov. Data (TKDD) 11(3), 26 (2017)

    Google Scholar 

  21. Şimşek, Ö., Barto, A.G.: Skill characterization based on betweenness. In: Advances in Neural Information Processing Systems, pp. 1497–1504 (2009)

    Google Scholar 

  22. Ufimtsev, V., Bhowmick, S.: Finding high betweenness centrality vertices in large networks. In: CSC14: The Sixth SIAM Workshop on Combinatorial Scientific Computing, p. 45 (2014)

    Google Scholar 

  23. Yan, G., Zhou, T., Hu, B., Fu, Z.Q., Wang, B.H.: Efficient routing on complex networks. Phys. Rev. E 73(4), 046108 (2006)

    Google Scholar 

  24. Yoshida, Y.: Almost linear-time algorithms for adaptive betweenness centrality using hypergraph sketches. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1416–1425. ACM (2014)

    Google Scholar 

Download references

Acknowledgements

The author would like to acknowledge the many useful ideas and contributions of Dr. Gunes Ercal and thank her sincerely for her help and support.

Author information

Authors and Affiliations

  1. Southern Illinois University Edwardsville, Edwardsville, IL, USA

    John Matta

Authors
  1. John Matta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John Matta .

Editor information

Editors and Affiliations

  1. University of Lyon 2, Lyon, France

    Chantal Cherifi

  2. University of Burgundy, Dijon, France

    Hocine Cherifi

  3. École Normale Supérieure de Lyon, Lyon, France

    Márton Karsai

  4. University College London, London, United Kingdom

    Mirco Musolesi

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Matta, J. (2018). A Comparison of Approaches to Computing Betweenness Centrality for Large Graphs. In: Cherifi, C., Cherifi, H., Karsai, M., Musolesi, M. (eds) Complex Networks & Their Applications VI. COMPLEX NETWORKS 2017. Studies in Computational Intelligence, vol 689. Springer, Cham. https://doi.org/10.1007/978-3-319-72150-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-72150-7_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72149-1

  • Online ISBN: 978-3-319-72150-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation