Abstract
Many real-life data sets, such as social, biological and communication networks are naturally and easily modeled as large labeled graphs. Finding patterns of interest in these graphs is an important task, but due to the nature of the data not all of the patterns need to be taken into account. Intuitively, if a pattern has high connectivity, it implies that there is a strong connection between data items. In this paper, we present a novel algorithm for finding frequent graph patterns with prescribed connectivity in large single-graph data sets. We also show how this algorithm can be adapted to a dynamic environment where the data changes over time. We prove that the suggested algorithm generates no more candidate graphs than any other algorithm whose graph extension procedure we employ.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bixby, R.E.: The minimum number of edges and vertices in a graph with edge connectivity n and m n-bonds. Networks 5, 253–298 (1975)
De Vitis, A.: The cactus representation of all minimum cuts in a weighted graph. Technical Report 454, IASI-CNR (1997)
Dinits, E.A., Karzanov, A.V., Lomonosov, M.V.: On the structure of a family of minimal weighted cuts in a graph. In: Fridman, A.A. (ed.) Studies in Discrete Optimization, pp. 290–306. Nauka, Moscow (1976)
Fiedler, M., Borgelt, C.: Support computation for mining frequent subgraphs in a single graph. In: International Workshop on Mining and Learning with Graphs (2007)
Fleischer, L.: Building Chain and Cactus Representations of All Minimum Cuts from Hao-Orlin in the Same Asymptotic Run Time. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds.) IPCO 1998. LNCS, vol. 1412, pp. 294–309. Springer, Heidelberg (1998)
Gomory, R.E., Hu, T.C.: Multi-terminal network flows. J. Soc. Indust. Appl. Math. 9(4), 551–570 (1991)
Horváth, T., Ramon, J.: Efficient frequent connected subgraph mining in graphs of bounded tree-width. Theor. Comput. Sci. 411(31-33), 2784–2797 (2010)
Karger, D.R., Stein, C.: A new approach to the minimum cut problem. Journal of the ACM 43(4), 601–640 (1996)
Karger, D.R., Panigrahi, D.: A near-linear time algorithm for constructing a cactus representation of minimum cuts. In: SODA 2009, pp. 246–255 (2009)
Karzanov, A.V., Timofeev, E.A.: Efficient algorithms for finding all minimal edge cuts of a nonoriented graph. Cybernetics 22, 156–162 (1986); Translated from Kibernetika 2, 8–12 (1986)
Kuramochi, M., Karypis, G.: Frequent Subgraph Discovery. In: ICDM 2001, pp. 313–320 (2001)
Nagamochi, H., Kameda, T.: Canonical cactus representation for minimum cuts. Japan Journal of Industrial Appliel Mathematics 11, 343–361 (1994)
Papadopoulos, A., Lyritsis, A., Manolopoulos, Y.: Skygraph: an algorithm for important subgraph discovery in relational graphs. Journal of Data Mining and Knowledge Discovery 17(1) (2008)
Seeland, M., Girschick, T., Buchwald, F., Kramer, S.: Online Structural Graph Clustering Using Frequent Subgraph Mining. In: Balcázar, J.L., Bonchi, F., Gionis, A., Sebag, M. (eds.) ECML PKDD 2010, Part III. LNCS, vol. 6323, pp. 213–228. Springer, Heidelberg (2010)
Yan, X., Zhou, X.J., Han, J.: Mining Closed Relational Graphs with Connectivity Constraints. In: ICDE 2005, pp. 357–358 (2005)
Zhang, S., Li, S., Yang, J.: GADDI: distance index based subgraph matching in biological networks. In: EDBT 2009, pp. 192–203 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vanetik, N. (2013). Mining Graphs of Prescribed Connectivity. In: Fred, A., Dietz, J.L.G., Liu, K., Filipe, J. (eds) Knowledge Discovery, Knowledge Engineering and Knowledge Management. IC3K 2011. Communications in Computer and Information Science, vol 348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37186-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-37186-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37185-1
Online ISBN: 978-3-642-37186-8
eBook Packages: Computer ScienceComputer Science (R0)