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Modularity-Driven Clustering of Dynamic Graphs

  • Robert Görke
  • Pascal Maillard
  • Christian Staudt
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6049)

Abstract

Maximizing the quality index modularity has become one of the primary methods for identifying the clustering structure within a graph. As contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work we pioneer the NP-hard problem of online dynamic modularity maximization. We develop scalable dynamizations of the currently fastest and the most widespread static heuristics and engineer a heuristic dynamization of an optimal static algorithm. Our algorithms efficiently maintain a modularity-based clustering of a graph for which dynamic changes arrive as a stream. For our quickest heuristic we prove a tight bound on its number of operations. In an experimental evaluation on both a real-world dynamic network and on dynamic clustered random graphs, we show that the dynamic maintenance of a clustering of a changing graph yields higher modularity than recomputation, guarantees much smoother clustering dynamics and requires much lower runtimes. We conclude with giving recommendations for the choice of an algorithm.

Keywords

Random Graph Graph Cluster Dynamic Algorithm Dynamic Graph Dynamic Maintenance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Görke, R., Maillard, P., Staudt, C., Wagner, D.: Modularity-Driven Clustering of Dynamic Graphs. Technical report, Universität Karlsruhe (TH), Informatik, TR 2010-5 (2010)Google Scholar
  2. 2.
    Brandes, U., Delling, D., Gaertler, M., Görke, R., Höfer, M., Nikoloski, Z., Wagner, D.: On Modularity Clustering. IEEE TKDE 20(2), 172–188 (2008)Google Scholar
  3. 3.
    Fortunato, S.: Community detection in graphs. Elsevier Phys. R 486(3-5) (2009)Google Scholar
  4. 4.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69(026113) (2004)Google Scholar
  5. 5.
    Keogh, E., Lonardi, S., Ratanamahatana, C.A.: Towards Parameter-Free Data Mining. In: Proc. of the 10th ACM SIGKDD Int. Conf., pp. 206–215. ACM, New York (2004)Google Scholar
  6. 6.
    Schaeffer, S.E., Marinoni, S., Särelä, M., Nikander, P.: Dynamic Local Clustering for Hierarchical Ad Hoc Networks. In: Proc. of Sensor and Ad Hoc Communications and Networks, vol. 2, pp. 667–672. IEEE, Los Alamitos (2006)CrossRefGoogle Scholar
  7. 7.
    Blondel, V., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. Journal of Statistical Mechanics: The. and Exp. 2008(10)Google Scholar
  8. 8.
    Delling, D., Görke, R., Schulz, C., Wagner, D.: ORCA Reduction and ContrAction Graph Clustering. In: Goldberg, A.V., Zhou, Y. (eds.) AAIM 2009. LNCS, vol. 5564, pp. 152–165. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Görke, R., Hartmann, T., Wagner, D.: Dynamic Graph Clustering Using Minimum-Cut Trees. In: Dehne, F., et al. (eds.) WADS 2009. LNCS, vol. 5664, pp. 339–350. Springer, Heidelberg (2009)Google Scholar
  10. 10.
    Hopcroft, J.E., Khan, O., Kulis, B., Selman, B.: Tracking Evolving Communities in Large Linked Networks. Proceedings of the National Academy of Science of the United States of America 101 (April 2004)Google Scholar
  11. 11.
    Palla, G., Barabási, A.L., Vicsek, T.: Quantifying social group evolution. Nature 446, 664–667 (2007)CrossRefGoogle Scholar
  12. 12.
    Aggarwal, C.C., Yu, P.S.: Online Analysis of Community Evolution in Data Streams. In: [31]Google Scholar
  13. 13.
    Sun, J., Yu, P.S., Papadimitriou, S., Faloutsos, C.: GraphScope: Parameter-Free Mining of Large Time-Evolving Graphs. In: Proc. of the 13th ACM SIGKDD Int. Conference, pp. 687–696. ACM Press, New York (2007)Google Scholar
  14. 14.
    Hübner, F.: The Dynamic Graph Clustering Problem - ILP-Based Approaches Balancing Optimality and the Mental Map. Master’s thesis, Universität Karlsruhe (TH), Fakultät für Informatik (May 2008)Google Scholar
  15. 15.
    Chakrabarti, D., Kumar, R., Tomkins, A.S.: Evolutionary Clustering. In: Proc. of the 12th ACM SIGKDD Int. Conference, pp. 554–560. ACM Press, New York (2006)Google Scholar
  16. 16.
    Schaeffer, S.E.: Graph Clustering. Computer Science Review 1(1), 27–64 (2007)CrossRefMathSciNetGoogle Scholar
  17. 17.
    White, S., Smyth, P.: A Spectral Clustering Approach to Finding Communities in Graphs. In: [31], pp. 274–285Google Scholar
  18. 18.
    Pons, P., Latapy, M.: Computing Communities in Large Networks Using Random Walks. Journal of Graph Algorithms and Applications 10(2), 191–218 (2006)zbMATHMathSciNetGoogle Scholar
  19. 19.
    van Dongen, S.M.: Graph Clustering by Flow Simulation. PhD thesis, University of Utrecht (2000)Google Scholar
  20. 20.
    Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Physical Review E 70(066111) (2004)Google Scholar
  21. 21.
    Brandes, U., Erlebach, T. (eds.): Network Analysis: Methodological Foundations. LNCS, vol. 3418. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  22. 22.
    Fortunato, S., Barthélemy, M.: Resolution limit in community detection. PNAS 104(1), 36–41 (2007)CrossRefGoogle Scholar
  23. 23.
    Newman, M.E.J.: Analysis of Weighted Networks. P. R. E 70(056131), 1–9 (2004)Google Scholar
  24. 24.
    Görke, R., Gaertler, M., Hübner, F., Wagner, D.: Computational Aspects of Lucidity-Driven Graph Clustering. JGAA 14(2) (2010)Google Scholar
  25. 25.
    Delling, D., Gaertler, M., Görke, R., Wagner, D.: Engineering Comparators for Graph Clusterings. In: Fleischer, R., Xu, J. (eds.) AAIM 2008. LNCS, vol. 5034, pp. 131–142. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  26. 26.
    Noack, A., Rotta, R.: Multi-level Algorithms for Modularity Clustering. In: Vahrenhold, J. (ed.) SEA 2009. LNCS, vol. 5526, pp. 257–268. Springer, Heidelberg (2009)Google Scholar
  27. 27.
    Görke, R., Staudt, C.: A Generator for Dynamic Clustered Random Graphs. Technical report, Universität Karlsruhe (TH), Informatik, TR 2009-7 (2009)Google Scholar
  28. 28.
    Brandes, U., Gaertler, M., Wagner, D.: Experiments on Graph Clustering Algorithms. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 568–579. Springer, Heidelberg (2003)Google Scholar
  29. 29.
    Guimerà, R., Amaral, L.A.N.: Functional Cartography of Complex Metabolic Networks. Nature 433, 895–900 (2005)CrossRefGoogle Scholar
  30. 30.
    Good, B.H., de Montjoye, Y., Clauset, A.: The performance of modularity maximization in practical contexts. arxiv.org/abs/0910.0165 (2009)Google Scholar
  31. 31.
    Proceedings of the fifth SIAM International Conference on Data Mining. SIAM, Philadelphia (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Robert Görke
    • 1
  • Pascal Maillard
    • 2
  • Christian Staudt
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie Curie (Paris VI)ParisFrance

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