Efficiently Enumerating All Connected Induced Subgraphs of a Large Molecular Network

  • Sean Maxwell
  • Mark R. Chance
  • Mehmet Koyutürk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8542)


In systems biology, the solution space for a broad range of problems is composed of sets of functionally associated biomolecules. Since connectivity in molecular interaction networks is an indicator of functional association, such sets can be identified from connected induced subgraphs of molecular interaction networks. Applications typically quantify the relevance (e.g., modularity, conservation, disease association) of connected subnetworks using an objective function and use a search algorithm to identify sets of subnetworks that maximize this objective function. Efficient enumeration of connected subgraphs of a large graph is therefore useful for these applications, and many existing search algorithms can be used for this purpose. However, there is a lack of non-heuristic algorithms that minimize the total number of subgraphs evaluated during the search for subgraphs that maximize the objective function. Here, we propose and evaluate an algorithm that reduces the computations necessary to enumerate subgraphs that maximize an objective function given a monotonically decreasing bounding function.


connected subgraph enumeration protein interaction networks branch-and-bound algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avis, D., Fukuda, K.: Reverse search for enumeration. Discrete Applied Mathematics (1993)Google Scholar
  2. 2.
    Bollobas, B.: Hereditary properties of graphs asymptotic enumeration global structure and colouring. Documenta Mathematica, 333–342 (1998)Google Scholar
  3. 3.
    Chowdhury, S., Koyuturk, M.: Identification of coordinately dysregulated subnetworks in complex phenotypes. In: Berger, B. (ed.) Pacific Symposium on Biocomputing, pp. 133–144 (2010)Google Scholar
  4. 4.
    Chowdhury, S., Nibbe, R., Chance, M., Koyuturk, M.: Subnetwork state functions define dysregulated subnetworks in cancer. Journal of Computational Biology 18(3), 263–281 (2011)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Chuang, H.Y., Lee, E., Yu-Tsueng, L.D., Ideker, T.: Network-based classification of breast cancer metastasis. Molecular Systems Biology (2007)Google Scholar
  6. 6.
    Dao, P., Wang, K., Collins, C., Ester, M., Lapuk, A., Sahinalp1, S.C.: Optimally discriminative subnetwork markers predict response to chemotherapy. Bioinformatics (July 2011)Google Scholar
  7. 7.
    Flannick, J., Novak, A., Srinivasan, B., McAdams, H., Batzoglou, S.: Graemlin: General and robust alignment of multiple large interaction networks. Genome Research (2006)Google Scholar
  8. 8.
    Hopcroft, J., Tarjan, R.: Efficient algorithms for graph manipulation. Communications of the ACM 16(6) (1973)Google Scholar
  9. 9.
    Ideker, T., Ozier, O., Schwikowski, B., Siegel, A.F.: Discovering regulatory and signalling circuits in molecular interaction networks. Bioinformatics 18(suppl. 1), S233–S240 (2002),
  10. 10.
    Jia, P., Zheng, S., Long, J., Zheng, W., Zhao, Z.: dmGWAS: dense module searching for genome-wide association studies in protein-protein interaction networks. Bioinformatics 27(1), 95–102 (2011)CrossRefGoogle Scholar
  11. 11.
    Kalaev, M., Smoot, M., Ideker, T., Sharan, R.: Networkblast: comparative analysis of protein networks. Bioinformatics (2008)Google Scholar
  12. 12.
    Karakashian, S., Choueiry, B.Y., Hartke, S.G.: An algorithm for generating all connected subgraphs with k vertices of a graph (May 2013),
  13. 13.
    Kesheva, P., et al.: Human protein reference database: 2009 update. Nucleic Acids Research 37, 767–772 (2009)CrossRefGoogle Scholar
  14. 14.
    Knuth, D.: The Art of Computer Programming, Combinatorial Algorithms Part 1, vol. 4. Addison-Wesley (2012)Google Scholar
  15. 15.
    Konga, B., Yanga, T., Chenb, L., Qin Kuanga, Y., Wen Gua, J., Xiaa, X., Chenga, L., Hai Zhang, J.: Proteinprotein interaction network analysis and gene set enrichment analysis in epilepsy patients with brain cancer. Journal of Clinical Neuroscience (2013)Google Scholar
  16. 16.
    Koyutürk, M., Kim, Y., Subramaniam, S., Szpankowski, W., Grama, A.: Detecting conserved interaction patterns in biological networks. Journal of Computational Biology (2006)Google Scholar
  17. 17.
    Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: Densification and shrinking diameters. ACM Transactions on Knowledge Discovery from Data (2007)Google Scholar
  18. 18.
    Patel, V., Gokulrangan, G., Chowdhury, S., Chen, Y., Sloan, A., Koyutrk, M., Barnholtz-Sloan, J., Chance, M.: Network signatures of survival in glioblastoma multiforme. PLOS Computational Biology 9 (2013)Google Scholar
  19. 19.
    Rymon, R.: Search through systematic set enumeration. Tech. rep., University of Pennsylvania (August 1992)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sean Maxwell
    • 1
  • Mark R. Chance
    • 1
  • Mehmet Koyutürk
    • 1
    • 2
  1. 1.Center for Proteomics and BioinformaticsCase Western Reserve UniversityClevelandUSA
  2. 2.Department of Electrical Engineering and Computer ScienceCase Western Reserve UniversityClevelandUSA

Personalised recommendations