Fully-Dynamic Hierarchical Graph Clustering Using Cut Trees

  • Christof Doll
  • Tanja Hartmann
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)


Algorithms or target functions for graph clustering rarely admit quality guarantees or optimal results in general. However, a hierarchical clustering algorithm by Flake et al., which is based on minimum s-t-cuts whose sink sides are of minimum size, yields such a provable guarantee. We introduce a new degree of freedom to this method by allowing arbitrary minimum s-t-cuts and show that this unrestricted algorithm is complete, i.e., any clustering hierarchy based on minimum s-t-cuts can be found by choosing the right cuts. This allows for a more comprehensive analysis of a graph’s structure. Additionally, we present a dynamic version of the unrestricted approach which employs this new degree of freedom to maintain a hierarchy of clusterings fulfilling this quality guarantee and effectively avoid changing the clusterings.


Dynamic Version Graph Cluster Hierarchical Cluster Algorithm Cluster Hierarchy Quality Guarantee 
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., Erlebach, T. (eds.): Network Analysis: Methodological Foundations LNCS, vol. 3418. Springer, Heidelberg (2005)zbMATHGoogle 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.
    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.
    Gusfield, D.: Very simple methods for all pairs network flow analysis. SIAM Journal on Computing 19(1), 143–155 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kannan, R., Vempala, S., Vetta, A.: On Clusterings: Good, Bad and Spectral. JACM 51(3), 497–515 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Saha, B., Mitra, P.: Dynamic Algorithm for Graph Clustering Using Minimum Cut Tree. In: Proc. of the 2007 SIAM Int. Conf. on Data Mining, pp. 581–586 (2007)Google Scholar
  8. 8.
    Görke, R., Hartmann, T., Wagner, D.: Dynamic Graph Clustering Using Minimum-Cut Trees. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 339–350. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Doll, C.: Hierarchical Cut Clustering in Dynamic Scenarios. Student Research Project, KIT Karlsruhe Institute of Technology, Department of Informatics (February 2011),
  10. 10.
    Doll, C., Hartmann, T., Wagner, D.: Fully-Dynamic Hierarchical Graph Clustering Using Cut Trees. Karlsruhe Reports in Informatics 2011-10, KIT Karlsruhe Institute of Technology (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christof Doll
    • 1
  • Tanja Hartmann
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Department of InformaticsKarlsruhe Institute of Technology (KIT)Germany

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