Novel Approaches for Analyzing Biological Networks
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This paper proposes clique relaxations to identify clusters in biological networks. In particular, the maximum n-clique and maximum n-club problems on an arbitrary graph are introduced and their recognition versions are shown to be NP-complete. In addition, integer programming formulations are proposed and the results of sample numerical experiments performed on biological networks are reported.
Keywordsn-cliques n-clubs clique relaxations social networks biological networks
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- R.D. Alba, “A graph-theoretic definition of a sociometric clique,” Journal of Mathematical Sociology, vol. 3, pp. 113–126, 1973.Google Scholar
- E. Almaas and A.-L. Barabási, “Power laws in biological networks,” in E. Koonin (Ed.), Power Laws, Scalefree Networks and Genome Biology, Landes Bioscience. To appear, 2005.Google Scholar
- J. Arquilla and D. Ronfeldt, “What Next for Networks and Netwars?,” in J. Arquilla and D. Ronfeldt (Eds.), Networks and Netwars: The Future of Terror, Crime, and Militancy. RAND Corporation, 2001, pp. 311–361.Google Scholar
- I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo, “The maximum clique problem,” in D.-Z. Du and P.M. Pardalos (Eds.), Handbook of Combinatorial Optimization. Dordrecht, The Netherlands, Kluwer Academic Publishers, 1999, pp. 1–74.Google Scholar
- BRITE, 2005, ȜBiomolecular Relations in Information Transmission and Expression. Generalized protein interactions,” http://www.genome.jp/brite/generalized_interactions.html. Accessed March 2005.
- CPLEX, “ILOG CPLEX,” http://www.ilog.com/products/cplex/. Accessed March 2005.
- R.H. Davis, “Social Network Analysis: An Aid in Conspiracy Investigations,” FBI Law Enforcement Bulletin, pp. 11–19, 1981.Google Scholar
- I. Fischer and T. Meinl, “Graph Based Molecular Data Mining–-An Overview,” in W. Thissen, P. Wieringa, M. Pantic, and M. Ludema (Eds.), IEEE SMC 2004 Conference Proceedings 2004, pp. 4578–4582.Google Scholar
- M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness. New York: W.H. Freeman and Company, 1979.Google Scholar
- Graphviz, “Graph Visualization Software,” http://www.graphviz.org/About.php. Accessed March 2005.
- F. Harary and I.C. Ross, “A procedure for clique detection using the group matrix,” Sociometry, vol. 20, pp. 205–215, 1957.Google Scholar
- D. Jiang, C. Tang, and A. Zhang, “Cluster Analysis for Gene Expression Data: A Survey,” vol. 16, no. 11, pp. 1370–1386, 2004.Google Scholar
- P. Krishna, N. Vaidya, M. Chatterjee, and D. Pradhan, “A cluster-based approach for routing in dynamic networks,” in ACM SIGCOMM Computer Communication Review, 1997, pp. 49–65.Google Scholar
- R.D. Luce and A.D. Perry, “A method of matrix analysis of group structure,” Psychometrika, vol. 14, pp. 95–116, 1949.Google Scholar
- X. Peng, M.A. Langston, A.M. Saxton, N.E. Baldwin, and J.R. Snoddy, “Detecting network motifs in gene co-expression networks,” 2004.Google Scholar
- J.C. Rain, L. Selig, H.D. Reuse, V. Battaglia, C. Reverdy, S. Simon, G. Lenzen, F. Petel, J. Wojcik, V. Schachter, Y. Chemama, A. Labigne, and P. Legrain, “The protein-protein interaction map of Helicobacter pylori,” Nature vol. 409, no. 6817, pp. 211–215, 2004. Erratum in: Nature 409(6820):553 and 409(6821):743, 2001.CrossRefGoogle Scholar
- T. Washio and H. Motoda, “State of the art of graph-based data mining,” SIGKDD Explor. Newsl., vol. 5, no. 1, pp. 59–68, 2003.Google Scholar
- S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications. Cambridge University Press, 1994.Google Scholar
- D. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton, NJ: Princeton University Press, 1999.Google Scholar