Skip to main content
SpringerLink
Log in

Partitioning large networks without breaking communities

  • Regular Paper
  • Published:
Knowledge and Information Systems Aims and scope Submit manuscript

Abstract

The identification of cohesive communities is a key process in social network analysis. However, the algorithms that are effective for finding communities do not scale well to very large problems, as their time complexity is worse than linear in the number of edges in the graph. This is an important issue for those interested in applying social network analysis techniques to very large networks, such as networks of mobile phone subscribers. In this respect, the contributions of this paper are twofold. First, we demonstrate these scaling issues using a prominent community-finding algorithm as a case study. Then, we show that a two-stage process, whereby the network is first decomposed into manageable subnetworks using a multilevel graph partitioning procedure, is effective in finding communities in networks with more than 106 nodes.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Paliouras G, Papatheodorou C, Karkaletsis V, Spyropoulos CD (2000) Clustering the users of large web sites into communities. In: Proceedings of seventh international conference on machine learning (ICML’00), pp 719–726

  2. Srivastava J, Cooley R, Deshpande M, Tan P (2000) Web usage mining: discovery and applications of usage patterns from Web data. ACM SIGKDD Explor Newslett 1: 12–23

    Article  Google Scholar 

  3. He Y, Cheung Hui S (2002) Mining a Web Citation Database for author co-citation analysis. Inf Process Manag 38: 491–508

    Article  MATH  Google Scholar 

  4. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69: 56–68

    Google Scholar 

  5. Palla G, Derenyi I, Farkas I, Vicsek T (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435: 814–818

    Article  Google Scholar 

  6. Gregory S (2007) An algorithm to find overlapping community structure in networks. In: Proceedings of 11th European conference on principles and practice of knowledge discovery in databases (PKDD’07), pp 91–102

  7. Abello J, Pardalos PM, Resende MGC (1999) On maximum clique problems in very large graphs. In: External memory algorithms. DIMACS series in discrete mathematics and theoretical computer science, pp 119–130

  8. Dhillon I, Guan Y, Kulis B (2007) Weighted graph cuts without eigenvectors a multilevel approach. IEEE Trans Pattern Anal Mach Intell 29: 1944–1957

    Article  Google Scholar 

  9. Karp R (1972) Reducibility among combinatorial problems. Complex Comput Comput 43: 85–103

    MathSciNet  Google Scholar 

  10. Bron C, Kerbosch J (1973) Finding all cliques of an undirected graph. Commun ACM 16: 575–577

    Article  MATH  Google Scholar 

  11. Balas E, Yu CS (1986) Finding a maximum clique in an arbitrary graph. SIAM J Comput 15: 1054–1068

    Article  MathSciNet  MATH  Google Scholar 

  12. Wood DR (1997) An algorithm for finding a maximum clique in a graph. Oper Res Lett 21: 211–217

    Article  MathSciNet  MATH  Google Scholar 

  13. Alon N, Krivelevich M, Sudakov B (1998) Finding a large hidden clique in a random graph. In: 9th symposium on discrete algorithms (SODA), pp 91–102

  14. Östergård P (2002) A fast algorithm for the maximum clique problem. Discrete Appl Math 120: 197–207

    Article  MathSciNet  MATH  Google Scholar 

  15. Freeman L (1979) Centrality in social networks: conceptual clarification. Soc Netw 1: 215–239

    Article  Google Scholar 

  16. Granovetter M (1983) The strength of weak ties: a network theory revisited. Sociol Theory 1: 201–233

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Palla G, Dernyi I, Farkas I, Vicsek T (2005) Supplementary information: uncovering the overlapping community structure of complex networks in nature and society. Nature 1–12

  19. Shi J, Malik J (1997) Normalized cuts and image segmentation. In: Proceedings of IEEE conference on computer vision and pattern recognition (CVPR ’97), pp 731–737

  20. Chung FRK (1994) Spectral graph theory. In: CBMS conference on recent advances in spectral graph theory. Regional conference series in mathematics, vol 92, California State University, Fresno

  21. Pothen A, Simon HD, Liou KP (1990) Partitioning sparse matrices with eigenvectors of graphs. SIAM J Math Anal Appl 11: 430–452

    Article  MathSciNet  MATH  Google Scholar 

  22. Chan P, Schlag M, Zien J (1994) Spectral k-way ratio cut partitioning. IEEE Trans CAD Integr Circuits Syst 13: 1088–1096

    Article  Google Scholar 

  23. Karypis G, Kumar V (1999) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20: 359–392

    Article  MathSciNet  MATH  Google Scholar 

  24. Kernighan BW, Lin S (1970) An efficient heuristic procedure for partitioning graphs. Bell Syst Tech J 49: 291–307

    Google Scholar 

  25. McCallum A, Nigam K, Rennie J, Seymore K (2000) Automating the construction of internet portals with machine learning. Inf Retr J 3: 127–163

    Article  Google Scholar 

  26. Erdős P, Rényi A (1961) On the evolution of random graphs. Bull Inst Int Stat 38: 343–347

    Google Scholar 

  27. Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286: 509–512

    Article  MathSciNet  Google Scholar 

  28. Hakimi S (1962) On the realizability of a set of integers as degrees of the vertices of a graph. SIAM J Appl Math 10: 496–506

    Article  MathSciNet  MATH  Google Scholar 

  29. Narayanan H, Belkin M, Niyogi P (2007) On the relation between low density separation, spectral clustering and graph cuts. Adv Neural Inf Process Syst 19: 1025

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Informatics, University College Dublin, Dublin, Ireland

    Anand Narasimhamurthy, Derek Greene, Neil Hurley & Pádraig Cunningham

Authors
  1. Anand Narasimhamurthy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Derek Greene
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Neil Hurley
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pádraig Cunningham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pádraig Cunningham.

Additional information

The work was supported by Science Foundation Ireland Grant nos. 05/IN.1/I24 and 08/SRC/I407 and Enterprise Ireland Grant no. PC/2007/010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Narasimhamurthy, A., Greene, D., Hurley, N. et al. Partitioning large networks without breaking communities. Knowl Inf Syst 25, 345–369 (2010). https://doi.org/10.1007/s10115-009-0251-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10115-009-0251-x

Keywords

Search

Navigation