Graph Clustering with Local Density-Cut

  • Junming ShaoEmail author
  • Qinli Yang
  • Zhong Zhang
  • Jinhu Liu
  • Stefan Kramer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10827)


In this paper, we introduce a new graph clustering algorithm, called Dcut. The basic idea is to envision the graph clustering as a local density-cut problem. To identify meaningful communities in a graph, a density-connected tree is first constructed in a local fashion. Building upon the local intuitive density-connected tree, Dcut allows partitioning a graph into multiple densely tight-knit clusters effectively and efficiently. We have demonstrated that our method has several attractive benefits: (a) Dcut provides an intuitive criterion to evaluate the goodness of a graph clustering in a more precise way; (b) Building upon the density-connected tree, Dcut allows identifying high-quality clusters; (c) The density-connected tree also provides a connectivity map of vertices in a graph from a local density perspective. We systematically evaluate our new clustering approach on synthetic and real-world data sets to demonstrate its good performance.



This work is supported by the National Natural Science Foundation of China (61403062, 41601025, 61433014), Science-Technology Foundation for Young Scientist of SiChuan Province (2016JQ0007), State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (2017490211), National key research and development program (2016YFB0502300).


  1. 1.
    Ashburner, M., Ball, C.A., Blake, J.A., Botstein, D., Butler, H., Cherry, J.M., Harris, M.A.: Gene ontology: tool for the unification of biology. Nat. Genet. 25(1), 25 (2000)CrossRefGoogle Scholar
  2. 2.
    Böhm, C., Plant, C., Shao, J., Yang, Q.: Clustering by synchronization. In: ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 583–592 (2010)Google Scholar
  3. 3.
    Brohée, S., Faust, K., Lima-Mendez, G., Vanderstocken, G., Van Helden, J.: Network analysis tools: from biological networks to clusters and pathways. Nat. Protoc. 3(10), 1616–1629 (2008)CrossRefGoogle Scholar
  4. 4.
    Dongen, S.: A cluster algorithm for graphs. Technical report, Amsterdam (2000)Google Scholar
  5. 5.
    Evans, T.S.: Clique graphs and overlapping communities. J. Stat. Mech. Theory Exp. 12, P12037 (2010)CrossRefGoogle Scholar
  6. 6.
    Flake, G.W., Tarjan, R.E., Tsioutsiouliklis, K.: Graph clustering and minimum cut trees. Internet Math. 1(4), 385–408 (2004)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hagen, L., Kahng, A.B.: New spectral methods for ratio cut partitioning and clustering. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 11(9), 1074–1085 (1992)CrossRefGoogle Scholar
  8. 8.
    Hajiabadi, M., Zare, H., Bobarshad, H.: IEDC: an integrated approach for overlapping and non-overlapping community detection. Knowl.-Based Syst. 123, 188–199 (2017)CrossRefGoogle Scholar
  9. 9.
    Hennig, C., Hausdorf, B.: Design of dissimilarity measures: a new dissimilarity between species distribution areas. In: Batagelj, V., Bock, H.H., Ferligoj, A., Ẑiberna, A. (eds.) Data Science and Classification. STUDIES CLASS, pp. 29–37. Springer, Heidelberg (2006). Scholar
  10. 10.
    Karypis, G., Kumar, V.: Multilevelk-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 48(1), 96–129 (1998)CrossRefGoogle Scholar
  11. 11.
    Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Nat. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Newman, M.E.: Modularity and community structure in networks. Proc. Nat. Acad. Sci. 103(23), 8577–8582 (2006)CrossRefGoogle Scholar
  14. 14.
    Prim, R.C.: Shortest connection networks and some generalizations. Bell Labs Tech. J. 36(6), 1389–1401 (1957)CrossRefGoogle Scholar
  15. 15.
    Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66(336), 846–850 (1971)CrossRefGoogle Scholar
  16. 16.
    Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007)CrossRefGoogle Scholar
  17. 17.
    Shao, J.: Synchronization on Data Mining: A Universal Concept for Knowledge Discovery. LAP LAMBERT Academic Publishing, Saarbrücken (2012)Google Scholar
  18. 18.
    Shao, J., He, X., Yang, Q., Plant, C., Böhm, C.: Robust synchronization-based graph clustering. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds.) PAKDD 2013. LNCS (LNAI), vol. 7818, pp. 249–260. Springer, Heidelberg (2013). Scholar
  19. 19.
    Shao, J., Han, Z., Yang, Q., Zhou, T.: Community detection based on distance dynamics. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1075–1084 (2015)Google Scholar
  20. 20.
    Shao, J., Yang, Q., Dang, H.V., Schmidt, B., Kramer, S.: Scalable clustering by iterative partitioning and point attractor representation. ACM Trans. Knowl. Discov. Data 11(1), 5 (2016)CrossRefGoogle Scholar
  21. 21.
    Shao, J., Wang, X., Yang, Q., Plant, C., Böhm, C.: Synchronization-based scalable subspace clustering of high-dimensional data. Knowl. Inf. Syst. 52(1), 83–111 (2017)CrossRefGoogle Scholar
  22. 22.
    Shao, J., Huang, F., Yang, Q., Luo, G.: Robust prototype-based learning on data streams. IEEE Trans. Knowl. Data Eng. 30(5), 978–991 (2018)CrossRefGoogle Scholar
  23. 23.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRefGoogle Scholar
  24. 24.
    Strehl, A., Ghosh, J.: Cluster ensembles: a knowledge reuse framework for combining multiple partitions. J. Mach. Learn. Res. 3, 583–617 (2002)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of small-worldnetworks. Nature 393(6684), 440–442 (1998)CrossRefGoogle Scholar
  26. 26.
    Wu, Z., Leahy, R.: An optimal graph theoretic approach to data clustering: theory and its application to image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 15(11), 1101–1113 (1993)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Junming Shao
    • 1
    Email author
  • Qinli Yang
    • 1
  • Zhong Zhang
    • 1
  • Jinhu Liu
    • 1
  • Stefan Kramer
    • 2
  1. 1.School of Computer Science and Engineering, Big Data Reserach CenterUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Institute for Computer ScienceUniversity of MainzMainzGermany

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