Abstract
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.
Chapter PDF
Similar content being viewed by others
References
Aggarwal, C.C., Yu, P.S.: Online analysis of community evolution in data streams. In: SDM (2005)
Backstrom, L., Huttenlocher, D., Kleinberg, J., Lan, X.: Group formation in large social networks: membership, growth, and evolution. In: KDD (2006)
Borgwardt, K.M., Kriegel, H.-P., Wackersreuther, P.: Pattern mining in frequent dynamic subgraphs. In: ICDM (2006)
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)
Calders, T., Ramon, J., Van Dyck, D.: Anti-monotonic overlap-graph support measures. In: ICDM (2008)
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)
Ferlez, J., Faloutsos, C., Leskovec, J., Mladenic, D., Grobelnik, M.: Monitoring network evolution using MDL. In: ICDE (2008)
Fiedler, M., Borgelt, C.: Subgraph support in a single graph. In: Workshop on Mining Graphs and Complex Data, MGCS (2007)
Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301), 13–30 (1963)
Holder, L.B., Cook, D.J., Djoko, S.: Substucture discovery in the SUBDUE system. In: AAAI KDD Workshop (1994)
Inokuchi, A., Washio, T.: A fast method to mine frequent subsequences from graph sequence data. In: ICDM (2008)
Knuth, D.E.: The sandwich theorem. Electronic Journal of Combinatorics 1, 1 (1994)
Kuramochi, M., Karypis, G.: Frequent subgraph discovery. In: ICDM (2001)
Kuramochi, M., Karypis, G.: Finding frequent patterns in a large sparse graph. Data Mining and Knowledge Discovery 11(3), 243–271 (2005)
Leskovec, J., Backstrom, L., Kumar, R., Tomkins, A.: Microscopic evolution of social networks. In: KDD (2008)
Leskovec, J., Kleinberg, J.M., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: KDD (2005)
Liu, Z., Yu, J.X., Ke, Y., Lin, X., Chen, L.: Spotting significant changing subgraphs in evolving graphs. In: ICDM (2008)
Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: Graphscope: parameter-free mining of large time-evolving graphs. In: KDD (2007)
Sun, J., Tao, D., Faloutsos, C.: Beyond streams and graphs: dynamic tensor analysis. In: KDD (2006)
Tantipathananandh, C., Berger-Wolf, T., Kempe, D.: A framework for community identification in dynamic social networks. In: KDD (2007)
Vanetik, N., Shimony, S.E., Gudes, E.: Support measures for graph data. Data Mining Knowledge Discovery 13(2), 243–260 (2006)
Yan, X., Han, J.: gSpan: Graph-based substructure pattern mining. In: ICDM (2002)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Berlingerio, M., Bonchi, F., Bringmann, B., Gionis, A. (2009). Mining Graph Evolution Rules. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2009. Lecture Notes in Computer Science(), vol 5781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04180-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-04180-8_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04179-2
Online ISBN: 978-3-642-04180-8
eBook Packages: Computer ScienceComputer Science (R0)