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Significance-Driven Graph Clustering

  • Marco Gaertler
  • Robert Görke
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4508)

Abstract

Modularity, the recently defined quality measure for clusterings, has attained instant popularity in the fields of social and natural sciences. We revisit the rationale behind the definition of modularity and explore the founding paradigm. This paradigm is based on the trade-off between the achieved quality and the expected quality of a clustering with respect to networks with similar intrinsic structure. We experimentally evaluate realizations of this paradigm systematically, including modularity, and describe efficient algorithms for their optimization. We confirm the feasibility of the resulting generality by a first systematic analysis of the behavior of these realizations on both artificial and on real-world data, arriving at remarkably good results of community detection.

Keywords

Quality Index Greedy Algorithm Community Detection Graph Cluster Absolute Variant 
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.
    Gaertler, M.: Clustering. In: Brandes, U., Erlebach, T. (eds.) Network Analysis. LNCS, vol. 3418, pp. 178–215. Springer, Heidelberg (2005)Google Scholar
  2. 2.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69 (2004)Google Scholar
  3. 3.
    Newman, M.E.J.: A fast algorithm for detecting community structure in networks. Technical report, Department of Physics and Center for the Study of Complex Systems, University of Michigan (2003)Google Scholar
  4. 4.
    Fortunato, S., Barthelemy, M.: Resolution Limit in Community Detection. arXiv.org physics/0607100 (2006)Google Scholar
  5. 5.
    Ziv, E., Middendorf, M., Wiggins, C.: Information-Theoretic Approach to Network Modularity. Phys. Rev. E 71 (2005)Google Scholar
  6. 6.
    Muff, S., Rao, F., Caflisch, A.: Local Modularity Measure for Network Clusterizations. Phys. Rev. E 72 (2005)Google Scholar
  7. 7.
    Fine, P., Paolo, E.D., Philippides, A.: Spatially Constrained Networks and the Evolution of Modular Control Systems. In: 9th Intl. Conference on the Simulation of Adaptive Behavior, SAB (2006)Google Scholar
  8. 8.
    Newman, M.E.J.: Fast Algorithm for Detecting Community Structure in Networks. Physical Review E 69 (2004)Google Scholar
  9. 9.
    Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70 (2004)Google Scholar
  10. 10.
    Newman, M.: Modularity and Community Structure in Networks. Proceedings of the National Academy of Sciences, 8577–8582 (2005)Google Scholar
  11. 11.
    White, S., Smyth, P.: A Spectral Clustering Approach to Finding Communities in Graph. In: SIAM Data Mining Conference (2005)Google Scholar
  12. 12.
    Guimerà, R., Sales-Pardo, M., Amaral, L.A.N.: Modularity from Fluctuations in Random Graphs and Complex Networks. Physical Review E 70 (2004)Google Scholar
  13. 13.
    Reichardt, J., Bornholdt, S.: Statistical Mechanics of Community Detection. arXiv.org cond-mat/0603718 (2006)Google Scholar
  14. 14.
    Duch, J., Arenas, A.: Community Detection in Complex Networks using Extremal Optimization. Physical Review E 72 (2005)Google Scholar
  15. 15.
    Brandes, U., Delling, D., Gaertler, M., Görke, R., Hoefer, M., Nikoloski, Z., Wagner, D.: Maximizing modularity is hard, arxiv preprint (2006), http://arxiv.org/abs/physics/0608255
  16. 16.
    van Dongen, S.M.: Graph Clustering by Flow Simulation. PhD thesis, University of Utrecht (2000)Google Scholar
  17. 17.
    Coffin, M., Saltzmann, M.J.: Statistical analysis of computational tests of algorithms and heuristics. INFORMS Journal on Computing 12 (2000)Google Scholar
  18. 18.
    Newman, M.: Analysis of Weighted Networks. Technical report, Cornell University, Santa Fe Institute, University of Michigan (2004)Google Scholar
  19. 19.
    Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Technical report, University of New Mexico, University of Michigan (2004)Google Scholar
  20. 20.
    Brodal, G.S., Jacob, R.: Dynamic planar convex hull. In: FOCS, pp. 617–626 (2002)Google Scholar
  21. 21.
    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
  22. 22.
    Zachary, W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452–473 (1977)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Marco Gaertler
    • 1
  • Robert Görke
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Faculty of Informatics, Universität Karlsruhe (TH) 

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