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Mining most frequently changing component in evolving graphs

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Abstract

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.

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References

  1. Aggarwal, C.C., Zhao, Y., Yu, P.S.: Outlier detection in graph streams. In: ICDE (2011)

  2. Bifet, A., Gavaldà, R.: Mining frequent closed trees in evolving data streams. Intell. Data Anal. 15(1), 29–48 (2011)

    Google Scholar 

  3. Borgwardt, K.M., Kriegel, H.-P., Wackersreuther, P.: Pattern mining in frequent dynamic subgraphs. In: ICDM (2006)

  4. Chan, J., Bailey, J., Leckie, C.: Discovering and summarising regions of correlated spatio-temporal change in evolving graphs. In: ICDM Workshops (2006)

  5. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press and McGraw-Hill (2001)

  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. Diehl, S., Görg, C.: Graphs, they are changing. In: Graph Drawing (2002)

  8. Dinitz, Y., Nossenson, R.: Incremental maintenance of the 5-edge-connectivity classes of a graph. In: SWAT, pp. 272–285 (2000)

  9. Eppstein, D., Galil, Z., Italiano, G.F.: Dynamic graph algorithms. In: Algorithms and Theory of Computation Handbook (1999)

  10. Even, S, Shiloach, Y.: An on-line edge-deletion problem. J. ACM 28(1), 1–4 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  12. Frederickson, G.N.: Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Comput. 14(4), 252–257 (1985)

    MathSciNet  Google Scholar 

  13. Gomory, R.E., Hu, T.C.: Multi-terminal network flows. J. Soc. Ind. Appl. Math. 9(4), 551–570 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  15. Horst Bunke, M.K., Dickinson, P.J., Wallis, W.D.: A Graph-Theoretic Approach to Enterprise Network Dynamics. Birkhauser (2007)

  16. Inokuchi, A., Washio, T.: A fast method to mine frequent subsequences from graph sequence data. In: ICDM (2008)

  17. Jarry, A., Lotker, Z.: Connectivity in evolving graph with geometric properties. In: DIALM-POMC (2004)

  18. Lahiri, M., Berger-Wolf, T.Y.: Mining periodic behavior in dynamic social networks. In: ICDM (2008)

  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)

    Article  Google Scholar 

  20. Liu, Z., Yu, J.X., Ke, Y., Lin, X., Chen, L.: Spotting significant changing subgraphs in evolving graphs. In: ICDM (2008)

  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. Musial, K., Kazienko, P.: Social networks on the internet. World Wide Web 1–42. doi:10.1007/s11280-011-0155-z

  23. Ren, C., Lo, E., Kao, B., Zhu, X., Cheng, R.: On querying historical evolving graph sequences. In: VLDB (2011)

  24. Robardet, C.: Constraint-based pattern mining in dynamic graphs. In: ICDM (2009)

  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)

  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)

    Article  Google Scholar 

  27. Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: Graphscope: parameter-free mining of large time-evolving graphs. In: KDD (2007)

  28. Sun, J., Tao, D., Faloutsos, C.: Beyond streams and graphs: dynamic tensor analysis. In: KDD (2006)

  29. Tantipathananandh, C., Berger-Wolf, T.Y.: Constant-factor approximation algorithms for identifying dynamic communities. In: KDD (2009)

  30. Tantipathananandh, C., Berger-Wolf, T.Y., Kempe, D.: A framework for community identification in dynamic social networks. In: KDD (2007)

  31. Tong, H., Papadimitriou, S., Sun, J., Yu, P.S., Faloutsos, C.: Colibri: fast mining of large static and dynamic graphs. In: KDD (2008)

  32. Westbrook, J., Tarjan, R.E.: Maintaining bridge-connected and biconnected components on-line. Algorithmica 7(5&6), 433–464 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  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

    Article  Google Scholar 

  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

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Correspondence to Jeffrey Xu Yu.

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Yang, Y., Yu, J.X., Gao, H. et al. Mining most frequently changing component in evolving graphs. World Wide Web 17, 351–376 (2014). https://doi.org/10.1007/s11280-013-0204-x

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  • DOI: https://doi.org/10.1007/s11280-013-0204-x

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