Skip to main content
Log in

Novel Approaches for Analyzing Biological Networks

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • J. Abello, S. Butenko, P. Pardalos, and M. Resende, “Finding independent sets in a graph using continuous multivariable polynomial formulations,” Journal of Global Optimization, vol. 21, pp. 111–137, 2001.

    Article  Google Scholar 

  • 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.

  • L. Amaral, A. Scala, M. Barthélémy, and H. Stanley, “Classes of small-world networks,” in Proc. of National Academy of Sciences USA 2000, vol. 97, pp. 11149–11152.

    Article  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.

  • J.S. Bader, A. Chaudhuri, J.M. Rothberg, and J. Chant, “Gaining confidence in high-throughput protein interaction networks,” Nature Biotechnology vol. 22, no. 1, pp. 78–85, 2004.

    Article  PubMed  Google Scholar 

  • A.-L. Barabási and R. Albert, ȜEmergence of Scaling in Random Networks,” Science, vol. 286, pp. 509–512, 1999.

    Article  PubMed  MathSciNet  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.

  • S. Busygin, S. Butenko, and P.M. Pardalos, “A heuristic for the maximum independent set problem based on optimization of a quadratic over a sphere,” Journal of Combinatorial Optimization, vol. 6, pp. 287–297, 2002.

    Article  MathSciNet  Google Scholar 

  • R. Carraghan and P. Pardalos, “An Exact Algorithm for the Maximum Clique Problem,” Operations Research Letters, vol. 9, pp. 375–382, 1990.

    Article  Google Scholar 

  • H. Chen, W. Chung, J.J. Xu, G. Wang, Y. Qin, and M. Chau, “Crime Data Mining: A General Framework and Some Examples,” Computer, vol. 37, no. 4, pp. 50–56, 2004.

    Article  Google Scholar 

  • D.J. Cook, and L.B. Holder, “Graph-Based Data Mining,” IEEE Intelligent Systems, vol. 15, no. 2, pp. 32–41, 2000.

    Article  Google Scholar 

  • 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.

  • 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.

  • J. Gagneur, R. Krause, T. Bouwmeester, and G. Casari, “Modular decomposition of protein-protein interaction networks,” Genome Biology, vol. 5, no. 8, pp. R57.1–R57.12, 2004.

    Article  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 

  • H. Jeong, S.P. Mason, A.L. Barabási, and Z.N. Oltvai, “Centrality and lethality of protein networks,” Nature, vol. 411, pp. 41–42, 2001, http://www.nd.edu/networks/database/index.html.

    Article  PubMed  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.

  • R.D. Luce, “Connectivity and generalized cliques in sociometric group structure,” Psychometrika, vol. 15, pp. 169–190, 1950.

    PubMed  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 

  • R.J. Mokken, “Cliques, Clubs and Clans,” Quality and Quantity, 1979, vol. 13, pp. 161–173.

    Article  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.

  • 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.

    Article  Google Scholar 

  • V. Spirin and L.A. Mirny, “Protein complexes and functional modules in molecular networks,” in Proceedings of the National Academy of Sciences 2003, vol. 100, no. 21, pp. 12123–12128.

    Article  Google Scholar 

  • L. Terveen, W. Hill and B. Amento, “Constructing, organizing, and visualizing collections of topically related web resources,” ACM Transactions on Computer-Human Interaction, vol. 6, pp. 67–94, 1999.

    Article  Google 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.

  • D. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton, NJ: Princeton University Press, 1999.

    Google Scholar 

  • D. Watts and S. Strogatz, “Collective dynamics of “small-world” networks,” Nature, vol. 393, pp. 440–442, 1998.

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Balabhaskar Balasundaram.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Balasundaram, B., Butenko, S. & Trukhanov, S. Novel Approaches for Analyzing Biological Networks. J Comb Optim 10, 23–39 (2005). https://doi.org/10.1007/s10878-005-1857-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-005-1857-x

Keywords

Navigation