Skip to main content

Computing Communities in Large Networks Using Random Walks

  • Conference paper
Computer and Information Sciences - ISCIS 2005 (ISCIS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3733))

Included in the following conference series:

Abstract

Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, it works at various scales, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2log n) and space O(n 2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph).

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Wasserman, S., Faust, K.: Social network analysis. Cambridge University Press, Cambridge (1994)

    Google Scholar 

  2. Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)

    Article  Google Scholar 

  3. Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Newman, M.E.J.: The structure and function of complex networks. SIAM REVIEW 45, 167 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dorogovtsev, S., Mendes, J.: Evolution of Networks: From Biological Nets to the Internet and WWW. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  6. Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Physical Review E 70 (2004) 066111

    Google Scholar 

  7. Pothen, A., Simon, H.D., Liou, K.P.: Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11, 430–452 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49, 291–308 (1970)

    Google Scholar 

  9. Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. PNAS 99, 7821–7826 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69 (2004) 026113

    Google Scholar 

  11. Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. PNAS 101, 2658–2663 (2004)

    Article  Google Scholar 

  12. Fortunato, S., Latora, V., Marchiori, M.: Method to find community structures based on information centrality. Physical Review E 70, 56104 (2004)

    Article  Google Scholar 

  13. Newman, M.E.J.: Fast algorithm for detecting community structure in networks. Physical Review E 69, 66133 (2004)

    Article  Google Scholar 

  14. Donetti, L., Muñoz, M.A.: Detecting network communities: a new systematic and efficient algorithm. Journal of Statistical Mechanics 2004, 10012 (2004)

    Article  Google Scholar 

  15. Wu, F., Huberman, B.A.: Finding communities in linear time: A physics approach. The European Physical Journal B 38, 331–338 (2004)

    Article  Google Scholar 

  16. Reichardt, J., Bornholdt, S.: Detecting fuzzy community structures in complex networks with a potts model. Physical Review Letters 93 (2004) 218701

    Google Scholar 

  17. Bagrow, J., Bollt, E.: A local method for detecting communities. Physical Review E (2005) (to appear)

    Google Scholar 

  18. Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization. arXiv:cond-mat/0501368 (2005)

    Google Scholar 

  19. Gaume, B.: Balades aléatoires dans les petits mondes lexicaux. I3 Information Interaction Intelligence 4 (2004)

    Google Scholar 

  20. Fouss, F., Pirotte, A., Saerens, M.: A novel way of computing dissimilarities between nodes of a graph, with application to collaborative filtering. In: Workshop on Statistical Approaches for Web Mining (SAWM), Pisa, pp. 26–37 (2004)

    Google Scholar 

  21. Zhou, H., Lipowsky, R.: Network brownian motion: A new method to measure vertex-vertex proximity and to identify communities and subcommunities. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004. LNCS, vol. 3038, pp. 1062–1069. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  22. van Dongen, S.: Graph Clustering by Flow Simulation. PhD thesis, University of Utrecht (2000)

    Google Scholar 

  23. Lovász, L.: Random walks on graphs: a survey. In: Combinatorics, Paul Erdős is eighty, Budapest. Bolyai Soc. Math. Stud. János Bolyai Math. Soc., vol. 2, pp. 353–397 (1996); (Keszthely, 1993)

    Google Scholar 

  24. Simonsen, I., Eriksen, K.A., Maslov, S., Sneppen, K.: Diffusion on complex networks: a way to probe their large-scale topological structures. Physica A: Statistical Mechanics and its Applications 336, 163–173 (2004)

    Article  Google Scholar 

  25. Schulman, L.S., Gaveau, B.: Coarse grains: The emergence of space and order. Foundations of Physics 31, 713–731 (2001)

    Article  MathSciNet  Google Scholar 

  26. Gaveau, B., Lesne, A., Schulman, L.S.: Spectral signatures of hierarchical relaxation. Physics Letters A 258, 222–228 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  27. Ward, J.H.: Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association 58, 236–244 (1963)

    Article  MathSciNet  Google Scholar 

  28. Jambu, M., Lebeaux, M.: Cluster analysis and data analysis. North Holland Publishing, Amsterdam (1983)

    MATH  Google Scholar 

  29. Pons, P.: http://liafa.jussieu.fr/~pons/

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pons, P., Latapy, M. (2005). Computing Communities in Large Networks Using Random Walks. In: Yolum, p., Güngör, T., Gürgen, F., Özturan, C. (eds) Computer and Information Sciences - ISCIS 2005. ISCIS 2005. Lecture Notes in Computer Science, vol 3733. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11569596_31

Download citation

  • DOI: https://doi.org/10.1007/11569596_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29414-6

  • Online ISBN: 978-3-540-32085-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics