Mining Graph Evolution Rules

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5781)


In this paper we introduce graph-evolution rules, a novel type of frequency-based pattern that describe the evolution of large networks over time, at a local level. Given a sequence of snapshots of an evolving graph, we aim at discovering rules describing the local changes occurring in it. Adopting a definition of support based on minimum image we study the problem of extracting patterns whose frequency is larger than a minimum support threshold. Then, similar to the classical association rules framework, we derive graph-evolution rules from frequent patterns that satisfy a given minimum confidence constraint. We discuss merits and limits of alternative definitions of support and confidence, justifying the chosen framework. To evaluate our approach we devise GERM (Graph Evolution Rule Miner), an algorithm to mine all graph-evolution rules whose support and confidence are greater than given thresholds. The algorithm is applied to analyze four large real-world networks (i.e., two social networks, and two co-authorship networks from bibliographic data), using different time granularities. Our extensive experimentation confirms the feasibility and utility of the presented approach. It further shows that different kinds of networks exhibit different evolution rules, suggesting the usage of these local patterns to globally discriminate different kind of networks.


  1. 1.
    Aggarwal, C.C., Yu, P.S.: Online analysis of community evolution in data streams. In: SDM (2005)Google Scholar
  2. 2.
    Backstrom, L., Huttenlocher, D., Kleinberg, J., Lan, X.: Group formation in large social networks: membership, growth, and evolution. In: KDD (2006)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.
    Bringmann, B., Nijssen, S.: What is frequent in a single graph? In: Washio, T., Suzuki, E., Ting, K.M., Inokuchi, A. (eds.) PAKDD 2008. LNCS (LNAI), vol. 5012, pp. 858–863. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Calders, T., Ramon, J., Van Dyck, D.: Anti-monotonic overlap-graph support measures. In: ICDM (2008)Google Scholar
  6. 6.
    Desikan, P., Srivastava, J.: Mining temporally changing web usage graphs. In: Mobasher, B., Nasraoui, O., Liu, B., Masand, B. (eds.) WebKDD 2004. LNCS (LNAI), vol. 3932, pp. 1–17. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Ferlez, J., Faloutsos, C., Leskovec, J., Mladenic, D., Grobelnik, M.: Monitoring network evolution using MDL. In: ICDE (2008)Google Scholar
  8. 8.
    Fiedler, M., Borgelt, C.: Subgraph support in a single graph. In: Workshop on Mining Graphs and Complex Data, MGCS (2007)Google Scholar
  9. 9.
    Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301), 13–30 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Holder, L.B., Cook, D.J., Djoko, S.: Substucture discovery in the SUBDUE system. In: AAAI KDD Workshop (1994)Google Scholar
  11. 11.
    Inokuchi, A., Washio, T.: A fast method to mine frequent subsequences from graph sequence data. In: ICDM (2008)Google Scholar
  12. 12.
    Knuth, D.E.: The sandwich theorem. Electronic Journal of Combinatorics 1, 1 (1994)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Kuramochi, M., Karypis, G.: Frequent subgraph discovery. In: ICDM (2001)Google Scholar
  14. 14.
    Kuramochi, M., Karypis, G.: Finding frequent patterns in a large sparse graph. Data Mining and Knowledge Discovery 11(3), 243–271 (2005)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Leskovec, J., Backstrom, L., Kumar, R., Tomkins, A.: Microscopic evolution of social networks. In: KDD (2008)Google Scholar
  16. 16.
    Leskovec, J., Kleinberg, J.M., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: KDD (2005)Google Scholar
  17. 17.
    Liu, Z., Yu, J.X., Ke, Y., Lin, X., Chen, L.: Spotting significant changing subgraphs in evolving graphs. In: ICDM (2008)Google Scholar
  18. 18.
    Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: Graphscope: parameter-free mining of large time-evolving graphs. In: KDD (2007)Google Scholar
  19. 19.
    Sun, J., Tao, D., Faloutsos, C.: Beyond streams and graphs: dynamic tensor analysis. In: KDD (2006)Google Scholar
  20. 20.
    Tantipathananandh, C., Berger-Wolf, T., Kempe, D.: A framework for community identification in dynamic social networks. In: KDD (2007)Google Scholar
  21. 21.
    Vanetik, N., Shimony, S.E., Gudes, E.: Support measures for graph data. Data Mining Knowledge Discovery 13(2), 243–260 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Yan, X., Han, J.: gSpan: Graph-based substructure pattern mining. In: ICDM (2002)Google Scholar
  23. 23.
    Zhu, F., Yan, X., Han, J., Yu, P.S.: gPrune: A constraint pushing framework for graph pattern mining. In: Zhou, Z.-H., Li, H., Yang, Q. (eds.) PAKDD 2007. LNCS (LNAI), vol. 4426, pp. 388–400. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.ISTI - CNRPisaItaly
  2. 2.Yahoo! ResearchBarcelonaSpain
  3. 3.Katholieke Universiteit LeuvenBelgium

Personalised recommendations