# A FAST ALGORITHM FOR MINING GRAPHS OF PRESCRIBED CONNECTIVITY

### Natalia Vanetik

#### Abstract

Many real-life data sets, such as social and biological networks and biochemical data, are naturally and easily modeled as large labeled graphs. Finding patterns of interest in these graphs is an important task, 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 employ the Dinitz-Karzanov-Lomonosov cactus minimum cut structure of a graph to perform the task efficiently. We also prove that the suggested algorithm generates no more candidate graphs than any other algorithm whose graph extension procedure we use at the first step.

#### 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.
- Dinits, E. A., Karzanov, A. V., Lomonosov, M. V. ”On the structure of a family of minimal weighted cuts in a graph”, Studies in Discrete Optimization (in Russian) (ed. A.A. Fridman), Nauka, Moscow, 1976, 290-306.
- Fleischer, L. ”Building Chain and Cactus Representations of All Minimum Cuts from Hao-Orlin in the Same Asymptotic Run Time”, IPCO 1998: 294-309.
- Gomory, R. E., Hu, T. C. ”Multi-terminal network flows”, J. Soc. Indust. Appl. Math, 9(4):551-570, 1991.
- Horváth, T. and 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. and Stein, C. ”A new approach to the minimum cut problem”, Journal of the ACM, 43(4):601- 640, 1996.
- Karger, D. R. and Panigrahi, D. ”A near-linear time algorithm for constructing a cactus representation of minimum cuts”, SODA 2009, 246-255.
- Karzanov, A. V. and Timofeev, E. A. ”Efficient algorithms for finding all minimal edge cuts of a nonoriented graph”, Cybernetics, 22:156-162, 1986. Translated from Kibernetika 2 (1986) 8-12.
- Kuramochi, M. and Karypis, G. ”Frequent Subgraph Discovery”, ICDM 2001: 313-320.
- Papadopoulos, A., Lyritsis, A. and Manolopoulos, Y. ”Skygraph: an algorithm for important subgraph discovery in relational graphs”, Data Mining and Knowledge Discovery, 17(1), 2008.
- Seeland, M., Girschick, T., Buchwald, F. and Kramer, S. ”Online Structural Graph Clustering Using Frequent Subgraph Mining”, ECML/PKDD (3) 2010: 213-228.
- Yan, X., Zhou, X. J., and Han, J. ”Mining Closed Relational Graphs with Connectivity Constraints”, ICDE 2005: 357-358.
- Zhang, S., Li, S. and Yang, J. ”GADDI: distance index based subgraph matching in biological networks”, EDBT 2009: 192-203.

#### Paper Citation

#### in Harvard Style

Vanetik N. (2011). **A FAST ALGORITHM FOR MINING GRAPHS OF PRESCRIBED CONNECTIVITY** . In *Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)* ISBN 978-989-8425-79-9, pages 5-13. DOI: 10.5220/0003628300050013

#### in Bibtex Style

@conference{kdir11,

author={Natalia Vanetik},

title={A FAST ALGORITHM FOR MINING GRAPHS OF PRESCRIBED CONNECTIVITY},

booktitle={Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)},

year={2011},

pages={5-13},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003628300050013},

isbn={978-989-8425-79-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)

TI - A FAST ALGORITHM FOR MINING GRAPHS OF PRESCRIBED CONNECTIVITY

SN - 978-989-8425-79-9

AU - Vanetik N.

PY - 2011

SP - 5

EP - 13

DO - 10.5220/0003628300050013