Finding Modules in Networks with Non-modular Regions

  • Sharon Bruckner
  • Bastian Kayser
  • Tim O. F. Conrad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7933)


Most network clustering methods share the assumption that the network can be completely decomposed into modules, that is, every node belongs to (usually exactly one) module. Forcing this constraint can lead to misidentification of modules where none exist, while the true modules are drowned out in the noise, as has been observed e.g. for protein interaction networks. We thus propose a clustering model where networks contain both a modular region consisting of nodes that can be partitioned into modules, and a transition region containing nodes that lie between or outside modules. We propose two scores based on spectral properties to determine how well a network fits this model. We then evaluate three (partially adapted) clustering algorithms from the literature on random networks that fit our model, based on the scores and comparison to the ground truth. This allows to pinpoint the types of networks for which the different algorithms perform well.


Transition Region Module Density Module Size Find Module Dense Subgraph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bader, G.D., Hogue, C.W.: An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics 4 (2003)Google Scholar
  2. 2.
    Bagrow, J.P.: Communities and bottlenecks: Trees and treelike networks have high modularity. Phys. Rev. E 85, 066118 (2012)Google Scholar
  3. 3.
    Bovier, A., Eckhoff, M., Gayrard, V., Klein, M.: Metastability and low lying spectra in reversible markov chains. Comm. Math. Phys. 228, 219–255 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Brohée, S., Van Helden, J.: Evaluation of clustering algorithms for protein-protein interaction networks. BMC Bioinformatics 7, 488 (2006)CrossRefGoogle Scholar
  5. 5.
    Enright, A.J., Van Dongen, S., Ouzounis, C.A.: An efficient algorithm for large-scale detection of protein families. Nucleic Acids Research 30(7), 1575–1584 (2002)CrossRefGoogle Scholar
  6. 6.
    Feng, Z., Xu, X., Yuruk, N., Schweiger, T.A.J.: A novel similarity-based modularity function for graph partitioning. In: Song, I.-Y., Eder, J., Nguyen, T.M. (eds.) DaWaK 2007. LNCS, vol. 4654, pp. 385–396. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Han, J.-D.J., Bertin, N., Hao, T., et al.: Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature 430, 88–93 (2004)CrossRefGoogle Scholar
  8. 8.
    Khuller, S., Saha, B.: On finding dense subgraphs. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 597–608. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    King, A.D., Pržulj, N., Jurisica, I.: Protein complex prediction via cost-based clustering. Bioinformatics 20(17), 3013–3020 (2004)CrossRefGoogle Scholar
  10. 10.
    Krause, R., von Mering, C., Bork, P., Dandekar, T.: Shared components of protein complexes–versatile building blocks or biochemical artefacts? BioEssays 26(12), 1333–1343 (2004)CrossRefGoogle Scholar
  11. 11.
    Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Pattern Recognition Letters 69(2), 413–421 (2004)Google Scholar
  13. 13.
    Nicosia, V., Mangioni, G., Carchiolo, V., Malgeri, M.: Extending the definition of modularity to directed graphs with overlapping communities. Journal of Statistical Mechanics: Theory and Experiment 2009, 22 (2008)Google Scholar
  14. 14.
    Palla, G., et al.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 1–10 (2005)CrossRefGoogle Scholar
  15. 15.
    Pu, S., Wong, J., Turner, B., Cho, E., Wodak, S.J.: Up-to-date catalogues of yeast protein complexes. Nucleic Acids Research 37(3), 825–831 (2009)CrossRefGoogle Scholar
  16. 16.
    Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)CrossRefGoogle Scholar
  17. 17.
    Santo, F.: Community detection in graphs. Physics Reports 486(3-5), 75–174 (2010) ISSN 0370-1573MathSciNetCrossRefGoogle Scholar
  18. 18.
    Santos, J.M., Embrechts, M.: On the use of the Adjusted Rand Index as a metric for evaluating supervised classification. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds.) ICANN 2009, Part II. LNCS, vol. 5769, pp. 175–184. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Sarich, M., Schuette, C., Vanden-Eijnden, E.: Optimal fuzzy aggregation of networks. Multiscale Modeling and Simulation 8(4), 1535–1561 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Sarich, M., Djurdjevac, N., Bruckner, S., Conrad, T.O.F., Schütte, C.: Modularity revisited: A novel dynamics-based concept for decomposing complex networks. To Appear, Journal of Computational Dynamics (2012),
  21. 21.
    Satuluri, V., Parthasarathy, S., Ucar, D.: Markov clustering of protein interaction networks with improved balance and scalability. In: Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology, BCB 2010, pp. 247–256. ACM (2010)Google Scholar
  22. 22.
    Sawardecker, E.N., Sales-Pardo, M., Amaral, L.A.N.: Detection of node group membership in networks with group overlap. EPJ B 67, 277 (2009)CrossRefGoogle Scholar
  23. 23.
    Schütte, C., Sarich, M.: Metastability and Markov State Models in Molecular Dynamics. Submitted to Courant Lecture Notes (2013)Google Scholar
  24. 24.
    Sprinzak, E., Altuvia, Y., Margalit, H.: Characterization and prediction of protein-protein interactions within and between complexes. PNAS 103(40), 14718–14723 (2006)CrossRefGoogle Scholar
  25. 25.
    Weber, M., Rungsarityotin, W., Schliep, A.: Perron cluster analysis and its connection to graph partitioning for noisy data. ZIB Report, 04-39 (2004)Google Scholar
  26. 26.
    Xu, X., Yuruk, N., Feng, Z., Schweiger, T.A.J.: SCAN: a structural clustering algorithm for networks. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2007, pp. 824–833. ACM, New York (2007)CrossRefGoogle Scholar
  27. 27.
    Yu, L., Gao, L., Sun, P.G.: A hybrid clustering algorithm for identifying modules in protein protein interaction networks. Int. J. Data Min. Bioinformatics 4(5), 600–615 (2010)CrossRefGoogle Scholar
  28. 28.
    Zhang, S., Wang, R., Zhang, X.: Identification of overlapping community structure in complex networks using fuzzy cc-means clustering. Physica A: Statistical Mechanics and its Applications 374(1), 483–490 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sharon Bruckner
    • 1
  • Bastian Kayser
    • 1
  • Tim O. F. Conrad
    • 1
  1. 1.Institut für MathematikFreie Universität BerlinGermany

Personalised recommendations