World Wide Web

, Volume 17, Issue 3, pp 351–376 | Cite as

Mining most frequently changing component in evolving graphs

  • Yajun Yang
  • Jeffrey Xu YuEmail author
  • Hong Gao
  • Jian Pei
  • Jianzhong Li


Many applications see huge demands of finding important changing areas in evolving graphs. In this paper, given a series of snapshots of an evolving graph, we model and develop algorithms to capture the most frequently changing component (MFCC). Motivated by the intuition that the MFCC should capture the densest area of changes in an evolving graph, we propose a simple yet effective model. Using only one parameter, users can control tradeoffs between the “density” of the changes and the size of the detected area. We verify the effectiveness and the efficiency of our approach on real data sets systematically.


Detecting graph changes Evolving graphs 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aggarwal, C.C., Zhao, Y., Yu, P.S.: Outlier detection in graph streams. In: ICDE (2011)Google Scholar
  2. 2.
    Bifet, A., Gavaldà, R.: Mining frequent closed trees in evolving data streams. Intell. Data Anal. 15(1), 29–48 (2011)Google Scholar
  3. 3.
    Borgwardt, K.M., Kriegel, H.-P., Wackersreuther, P.: Pattern mining in frequent dynamic subgraphs. In: ICDM (2006)Google Scholar
  4. 4.
    Chan, J., Bailey, J., Leckie, C.: Discovering and summarising regions of correlated spatio-temporal change in evolving graphs. In: ICDM Workshops (2006)Google Scholar
  5. 5.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press and McGraw-Hill (2001)Google Scholar
  6. 6.
    Cui, Y., Pei, J., Tang, G., Luk, W.-S., Jiang, D., Hua, M.: Finding email correspondents in online social networks. World Wide Web 1–24. doi: 10.1007/s11280-012-0168-2
  7. 7.
    Diehl, S., Görg, C.: Graphs, they are changing. In: Graph Drawing (2002)Google Scholar
  8. 8.
    Dinitz, Y., Nossenson, R.: Incremental maintenance of the 5-edge-connectivity classes of a graph. In: SWAT, pp. 272–285 (2000)Google Scholar
  9. 9.
    Eppstein, D., Galil, Z., Italiano, G.F.: Dynamic graph algorithms. In: Algorithms and Theory of Computation Handbook (1999)Google Scholar
  10. 10.
    Even, S, Shiloach, Y.: An on-line edge-deletion problem. J. ACM 28(1), 1–4 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: Graph distances in the data-stream model. SIAM J. Comput. 38(5), 1709–1727 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Frederickson, G.N.: Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Comput. 14(4), 252–257 (1985)MathSciNetGoogle Scholar
  13. 13.
    Gomory, R.E., Hu, T.C.: Multi-terminal network flows. J. Soc. Ind. Appl. Math. 9(4), 551–570 (1961)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Henzinger, M.R.: A static 2-approximation algorithm for vertex connectivity and incremental approximation algorithms for edge and vertex connectivity. J. Algorithms 24(1), 194–220 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Horst Bunke, M.K., Dickinson, P.J., Wallis, W.D.: A Graph-Theoretic Approach to Enterprise Network Dynamics. Birkhauser (2007)Google Scholar
  16. 16.
    Inokuchi, A., Washio, T.: A fast method to mine frequent subsequences from graph sequence data. In: ICDM (2008)Google Scholar
  17. 17.
    Jarry, A., Lotker, Z.: Connectivity in evolving graph with geometric properties. In: DIALM-POMC (2004)Google Scholar
  18. 18.
    Lahiri, M., Berger-Wolf, T.Y.: Mining periodic behavior in dynamic social networks. In: ICDM (2008)Google Scholar
  19. 19.
    Liang, W., Brent, R.P., Shen, H.: Fully dynamic maintenance of k-connectivity in parallel. IEEE Trans. Parallel Distrib. Syst. 12(8), 846–864 (2001)CrossRefGoogle Scholar
  20. 20.
    Liu, Z., Yu, J.X., Ke, Y., Lin, X., Chen, L.: Spotting significant changing subgraphs in evolving graphs. In: ICDM (2008)Google Scholar
  21. 21.
    Musial, K., Budka, M., Juszczyszyn, K.: Creation and growth of online social network. World Wide Web 1–27. doi: 10.1007/s11280-012-0177-1
  22. 22.
    Musial, K., Kazienko, P.: Social networks on the internet. World Wide Web 1–42. doi: 10.1007/s11280-011-0155-z
  23. 23.
    Ren, C., Lo, E., Kao, B., Zhu, X., Cheng, R.: On querying historical evolving graph sequences. In: VLDB (2011)Google Scholar
  24. 24.
    Robardet, C.: Constraint-based pattern mining in dynamic graphs. In: ICDM (2009)Google Scholar
  25. 25.
    Schweller, R.T., Gupta, A., Parsons, E., Chen, Y.: Reversible sketches for efficient and accurate change detection over network data streams. In: Internet Measurement Conference (2004)Google Scholar
  26. 26.
    Shoubridge, P., Kraetzl, M., Wallis, W.D., Bunke, H.: Detection of abnormal change in a time series of graphs. J. Interconnect. Netw. 3(1–2), 85–101 (2002)CrossRefGoogle Scholar
  27. 27.
    Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: Graphscope: parameter-free mining of large time-evolving graphs. In: KDD (2007)Google Scholar
  28. 28.
    Sun, J., Tao, D., Faloutsos, C.: Beyond streams and graphs: dynamic tensor analysis. In: KDD (2006)Google Scholar
  29. 29.
    Tantipathananandh, C., Berger-Wolf, T.Y.: Constant-factor approximation algorithms for identifying dynamic communities. In: KDD (2009)Google Scholar
  30. 30.
    Tantipathananandh, C., Berger-Wolf, T.Y., Kempe, D.: A framework for community identification in dynamic social networks. In: KDD (2007)Google Scholar
  31. 31.
    Tong, H., Papadimitriou, S., Sun, J., Yu, P.S., Faloutsos, C.: Colibri: fast mining of large static and dynamic graphs. In: KDD (2008)Google Scholar
  32. 32.
    Westbrook, J., Tarjan, R.E.: Maintaining bridge-connected and biconnected components on-line. Algorithmica 7(5&6), 433–464 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    Wu, D., Ke, Y., Yu, J., Yu, P., Chen, L.: Leadership discovery when data correlatively evolve. World Wide Web 14, 1–25 (2011). doi: 10.1007/s11280-010-0095-z CrossRefGoogle Scholar
  34. 34.
    Yu, Z., Zhou, X., Zhang, D., Schiele, G., Becker, C.: Understanding social relationship evolution by using real-world sensing data. World Wide Web 1–14. doi: 10.1007/s11280-012-0189-x

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Yajun Yang
    • 1
  • Jeffrey Xu Yu
    • 2
    Email author
  • Hong Gao
    • 1
  • Jian Pei
    • 3
  • Jianzhong Li
    • 1
  1. 1.Harbin Institute of TechnologyHarbinPeople’s Republic of China
  2. 2.Chinese University of Hong KongHong KongHong Kong
  3. 3.Simon Fraser UniversityBurnabyCanada

Personalised recommendations