Dynamic Graph Clustering Using Minimum-Cut Trees

  • Robert Görke
  • Tanja Hartmann
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5664)


Algorithms or target functions for graph clustering rarely admit quality guarantees or optimal results in general. Based on properties of minimum-cut trees, a clustering algorithm by Flake et al. does however yield such a provable guarantee. We show that the structure of minimum-s-t-cuts in a graph allows for an efficient dynamic update of minimum-cut trees, and present a dynamic graph clustering algorithm that maintains a clustering fulfilling this quality quarantee, and that effectively avoids changing the clustering. Experiments on real-world dynamic graphs complement our theoretical results.


Static Algorithm Full Version Graph Cluster Dynamic Graph Edge Addition 
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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  1. 1.
    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
  2. 2.
    Brandes, U., Erlebach, T. (eds.): Network Analysis. LNCS, vol. 3418. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  3. 3.
    Flake, G.W., Tarjan, R.E., Tsioutsiouliklis, K.: Graph Clustering and Minimum Cut Trees. Internet Mathematics 1(4), 385–408 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gomory, R.E., Hu, T.: Multi-terminal network flows. Journal of the Society for Industrial and Applied Mathematics 9(4), 551–570 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Görke, R., Hartmann, T., Wagner, D.: Dynamic Graph Clustering Using Minimum-Cut Trees. Technical report, Informatics, Universität Karlsruhe (2009)Google Scholar
  6. 6.
    Gusfield, D.: Very simple methods for all pairs network flow analysis. SIAM Journal on Computing 19(1), 143–155 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hartmann, T.: Clustering Dynamic Graphs with Guaranteed Quality. Master’s thesis, Universität Karlsruhe (TH), Fakultät für Informatik (October 2008)Google Scholar
  8. 8.
    Kannan, R., Vempala, S., Vetta, A.: On Clusterings - Good, Bad and Spectral. In: Proc. of FOCS 2000, pp. 367–378 (2000)Google Scholar
  9. 9.
    Saha, B., Mitra, P.: Dynamic Algorithm for Graph Clustering Using Minimum Cut Tree. In: Proc. of the, SIAM Int. Conf. on Data Mining, pp. 581–586 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Robert Görke
    • 1
  • Tanja Hartmann
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Faculty of InformaticsUniversität Karlsruhe (TH), Karlsruhe Institute of Technology (KIT)Germany

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