Skip to main content
SpringerLink
Log in
Book cover

Annual Symposium on Theoretical Aspects of Computer Science

STACS 2005: STACS 2005 pp 533–544Cite as

Centrality Measures Based on Current Flow

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3404))

Abstract

We consider variations of two well-known centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the current-flow variant of closeness centrality is identical with another known measure, information centrality, and give improved algorithms for computing both measures exactly. Since running times and space requirements are prohibitive for large networks, we also present a randomized approximation scheme for current-flow betweenness.

Research partially supported by DFG under grant Br~2158/1-2.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

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. Technical Report BN 9/71, Stichting Mathematisch Centrum, Amsterdam (1971)

    Google Scholar 

  2. Beauchamp, M.A.: An improved index of centrality. Behavioral Science 10, 161–163 (1965)

    Article  Google Scholar 

  3. Bollobás, B.: Modern Graph Theory. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  4. Borgatti, S.P.: Centrality and Network Flow. Social Networks (to appear)

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  7. Cuthill, E.H., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 24th ACM National Conference, pp. 157–172 (1969)

    Google Scholar 

  8. Diaz, J., Petit, J., Serna, M.: A Survey of Graph Layout Problems. ACM Comput. Surv. 34, 313–356 (2002)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Freeman, L.C., Borgatti, S.P., White, D.R.: Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks 13, 141–154 (1991)

    Article  MathSciNet  Google Scholar 

  11. Godsil, C., Royle, G.: Algebraic Graph Theory. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  12. Golub, G.H., van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (1983)

    MATH  Google Scholar 

  13. Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  14. Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58, 13–30 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kinnersley, N.G.: The vertex separation number of a graph equals its path width. Information Processing Letters 42, 345–350 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kirchhoff, G.: Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der Linearen Vertheilung galvanischer Ströme geführt wird. Ann. Phys. Chem. 72, 497–508 (1847)

    Article  Google Scholar 

  17. Lengauer, T.: Black-white pebbles and graph separation. Acta Informatica 16, 465–475 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  18. Newman, M.E.J.: A Measure of betweenness centrality based on random walks (2003), http://arxiv.org/abs/cond-mat/0309045

  19. Rosenthal, A., Pino, J.A.: A generalized algorithm for centrality problems on trees. Journal of the ACM 36, 349–381 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  20. Stephenson, K.A., Zelen, M.: Rethinking centrality: methods and examples. Social Networks 11, 1–37 (1989)

    Article  MathSciNet  Google Scholar 

  21. Wang, J., Eppstein, D.: Fast approximation of centrality. In: Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms, pp. 228–229 (2001)

    Google Scholar 

  22. Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer & Information Science, University of Konstanz,  

    Ulrik Brandes & Daniel Fleischer

Authors
  1. Ulrik Brandes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Fleischer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Universität Stuttgart, FMI, Germany

    Volker Diekert

  2. LIF, CNRS & Univ. de Provence,, Marseille

    Bruno Durand

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brandes, U., Fleischer, D. (2005). Centrality Measures Based on Current Flow. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-31856-9_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24998-6

  • Online ISBN: 978-3-540-31856-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation