Skip to main content
SpringerLink
Log in

Beta Current Flow Centrality for Weighted Networks

  • Conference paper
  • First Online:
Computational Social Networks (CSoNet 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9197))

Included in the following conference series:

Abstract

Betweenness centrality is one of the basic concepts in the analysis of social networks. Initial definition for the betweenness of a node in a graph is based on the fraction of the number of geodesics (shortest paths) between any two nodes that given node lies on, to the total number of the shortest paths connecting these nodes. This method has quadratic complexity and does not take into account indirect paths. We propose a new concept of betweenness centrality for weighted network, beta current flow centrality, based on Kirchhoff’s law for electric circuits. In comparison with the original current flow centrality and alpha current flow centrality, this new measure can be computed for larger networks. The results of numerical experiments for some examples of networks, in particular, for the popular social network VKontakte as well as the comparison with PageRank method are presented.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann, R., Myerson, R.: Endogenous formation of links between players and coalitions: an application of the Shapley value. In: The Shapley value, pp. 175–191. Cambridge University Press (1988)

    Google Scholar 

  2. Avrachenkov, K., Litvak, N., Medyanikov, V., Sokol, M.: Alpha current flow betweenness centrality. In: Bonato, A., Mitzenmacher, M., Prałat, P. (eds.) WAW 2013. LNCS, vol. 8305, pp. 106–117. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Avrachenkov, K., Litvak, N., Nemirovsky, D., Smirnova, E., Sokol, M.: Quick detection of top-k personalized pagerank lists. In: Frieze, A., Horn, P., Prałat, P. (eds.) WAW 2011. LNCS, vol. 6732, pp. 50–61. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Avrachenkov, K.E., Filar J.A., Howlett, P.G.: Analytic Perturbation Theory and its Applications. SIAM (2013)

    Google Scholar 

  5. Borgatti, S.P., Everett, M.G., Freeman, L.C.: Ucinet for Windows: Software for Social Network Analysis. Harvard (2002)

    Google Scholar 

  6. Borm, P., Owen, G., Tijs, S.: On the position value for communication situations. SIAM J. on Disc. Math. 5(3), 305–320 (1992)

    Article  MathSciNet  Google Scholar 

  7. Borm, P., van den Nouweland, A., Tijs, S.: Cooperation and communication restrictions: a survey. In: Imperfections and Behavior in Economic Organizations. Kluwer (1994)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Brandes, U., Fleischer, D.: Centrality measures based on current flow. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 533–544. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Calvo, E., Lasaga, J., van den Nouweland, A.: Values of games with probabilistic graphs. Math. Social Sci. 37, 79–95 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  12. Jackson, M.O.: Allocation rules for network games. Games and Econ. Behav. 51(1), 128–154 (2005)

    Article  MATH  Google Scholar 

  13. Jackson, M.O., Wolinsky, J.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jackson, M.O.: Social and economic networks. Princeton University Press (2008)

    Google Scholar 

  15. Jamison, R.E.: Alternating Whitney sums and matchings in trees. Part 1. Disc. Math. 67, 177–189 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mazalov, V.: Mathematical Game Theory and Applications. Wiley (2014)

    Google Scholar 

  17. Mazalov, V.V., Trukhina, L.I.: Generating functions and the Myerson vector in communication networks. Disc. Math. and Appl. 24(5), 295–303 (2014)

    MathSciNet  Google Scholar 

  18. Myerson, R.B.: Graphs and cooperation in games. Math. Oper. Res. 2, 225–229 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  19. Newman, M.E.J.: A measure of betweenness centrality based on random walks. Social networks 27, 39–54 (2005)

    Article  Google Scholar 

  20. Opsahl, T., Agneessens, F., Skvoretz, J.: Node centrality in weighted networks: generalizing degree and shortest paths. Social Networks 32, 245–251 (2010)

    Article  Google Scholar 

  21. Slikker, M.: Link monotonic allocation schemes. Int. Game Theory Review 7(4), 473–489 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Slikker, M., Gilles, R.P., Norde, H., Tijs, S.: Directed networks, allocation properties and hierarchy formation. Math. Social Sci. 49(1), 55–80 (2005)

    Article  MathSciNet  Google Scholar 

  23. Talman, D., Yamamoto, Y.: Average tree solutions and subcore for acyclic graph games. J. Oper. Res. Soc. Japan 51(3), 187–201 (2008)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA, 2004 Route des Lucioles, Sophia-Antipolis, France

    Konstantin E. Avrachenkov

  2. Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, 11, Pushkinskaya St., Petrozavodsk, 185910, Russia

    Vladimir V. Mazalov

  3. Transbaikal State University, 30, Aleksandro-Zavodskaya St., Chita, 672039, Russia

    Bulat T. Tsynguev

Authors
  1. Konstantin E. Avrachenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir V. Mazalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bulat T. Tsynguev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Konstantin E. Avrachenkov .

Editor information

Editors and Affiliations

  1. Computer and Information Science and Engineering, University of Florida, Gainesville, Florida, USA

    My T. Thai

  2. Towsen University, Towson, Maryland, USA

    Nam P. Nguyen

  3. Chinese Academy of Sciences, Beijing, China

    Huawei Shen

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Avrachenkov, K.E., Mazalov, V.V., Tsynguev, B.T. (2015). Beta Current Flow Centrality for Weighted Networks. In: Thai, M., Nguyen, N., Shen, H. (eds) Computational Social Networks. CSoNet 2015. Lecture Notes in Computer Science(), vol 9197. Springer, Cham. https://doi.org/10.1007/978-3-319-21786-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21786-4_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21785-7

  • Online ISBN: 978-3-319-21786-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation