Discovery of Top-k Dense Subgraphs in Dynamic Graph Collections

  • Elena Valari
  • Maria Kontaki
  • Apostolos N. Papadopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7338)


Dense subgraph discovery is a key issue in graph mining, due to its importance in several applications, such as correlation analysis, community discovery in the Web, gene co-expression and protein-protein interactions in bioinformatics. In this work, we study the discovery of the top-k dense subgraphs in a set of graphs. After the investigation of the problem in its static case, we extend the methodology to work with dynamic graph collections, where the graph collection changes over time. Our methodology is based on lower and upper bounds of the density, resulting in a reduction of the number of exact density computations. Our algorithms do not rely on user-defined threshold values and the only input required is the number of dense subgraphs in the result (k). In addition to the exact algorithms, an approximation algorithm is provided for top-k dense subgraph discovery, which trades result accuracy for speed. We show that a significant number of exact density computations is avoided, resulting in efficient monitoring of the top-k dense subgraphs.


Priority Queue Graph Object Expiration Time Dense Subgraph Active Graph 
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.
    Aggarwal, C., Wang, H.: Managing and mining graph data. Springer (2010)Google Scholar
  2. 2.
    Aggarwal, C., Li, Y., Yu, P.S., Jin, R.: On dense pattern mining in graph streams. In: Proceedings of the 36th VLDB Conference, pp. 975–984 (2010)Google Scholar
  3. 3.
    Batagelj, V., Zaversnik, M.: An O(m) algorithm for cores decomposition of networks. CoRR, cs.DS/0310049 (2003)Google Scholar
  4. 4.
    Chen, L., Wang, C.: Continuous subgraph pattern search over certain and uncertain graph streams. IEEE Transactions on Knowledge and Data Engineering 22(8), 1093–1109 (2010)CrossRefGoogle Scholar
  5. 5.
    Cook, D.J., Holder, L.B. (eds.): Mining graph data. Wiley (2007)Google Scholar
  6. 6.
    Gibson, D., Kumar, R., Tomkins, A.: Discovering large dense subgraphs in massive graphs. In: Proceedings of the 31st VLDB Conference, pp. 721–732 (2005)Google Scholar
  7. 7.
    Goldberg, A.V.: Finding a maximum density subgraph. Technical Report CSD-84-171, University of Berkeley (1984)Google Scholar
  8. 8.
    Hu, H., Yan, X., Huang, Y., Han, J., Zhou, X.J.: Mining coherent dense subgraphs across massive biological networks for functional discovery. Bioinformatics 21(1), i213–i221 (2005)CrossRefGoogle Scholar
  9. 9.
    Kortsarz, G., Peleg, D.: Generating sparse 2-spanners. Journal of Algorithms 17(2), 222–236 (1994)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Luczak, T.: Size and connectivity of the k-core of a random graph. Discrete Mathematics 91(1), 61–68 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Mouratidis, K., Bakiras, S., Papadias, D.: Continuous monitoring of top-k queries over sliding windows. In: Proceedings of the ACM SIGMOD Conference, pp. 635–646 (2006)Google Scholar
  12. 12.
    Papadias, D., Tao, Y., Fu, G., Seeger, B.: Progressive skyline computation in database systems. ACM Transactions on Database Systems 30(1), 41–82 (2005)CrossRefGoogle Scholar
  13. 13.
    Saha, B., Hoch, A., Khuller, S., Raschid, L., Zhang, X.-N.: Dense Subgraphs with Restrictions and Applications to Gene Annotation Graphs. In: Berger, B. (ed.) RECOMB 2010. LNCS, vol. 6044, pp. 456–472. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Seidman, S.B.: Network structure and minimum degree. Social Networks 5, 269–287 (1983)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: GraphScope: parameter-free mining of large time-evolving graphs. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 687–696 (2007)Google Scholar
  16. 16.
    Tao, Y., Papadias, D.: Maintaining sliding window skylines on data streams. IEEE Transactions on Knowledge and Data Engineering 18(3), 377–391 (2006)CrossRefGoogle Scholar
  17. 17.
    Viger, F., Latapy, M.: Efficient and Simple Generation of Random Simple Connected Graphs with Prescribed Degree Sequence. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 440–449. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Elena Valari
    • 1
  • Maria Kontaki
    • 1
  • Apostolos N. Papadopoulos
    • 1
  1. 1.Data Engineering Lab., Department of InformaticsAristotle UniversityThessalonikiGreece

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