A Faster Algorithm for Detecting Network Motifs

  • Sebastian Wernicke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3692)


Motifs in a network are small connected subnetworks that occur in significantly higher frequencies than in random networks. They have recently gathered much attention as a useful concept to uncover structural design principles of complex networks. Kashtan et al. [Bioinformatics, 2004] proposed a sampling algorithm for efficiently performing the computationally challenging task of detecting network motifs. However, among other drawbacks, this algorithm suffers from sampling bias and is only efficient when the motifs are small (3 or 4 nodes). Based on a detailed analysis of the previous algorithm, we present a new algorithm for network motif detection which overcomes these drawbacks. Experiments on a testbed of biological networks show our algorithm to be orders of magnitude faster than previous approaches. This allows for the detection of larger motifs in bigger networks than was previously possible, facilitating deeper insight into the field.


Random Graph Random Network Input Graph Network Motif Degree Sequence 
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.
    Albert, I., Albert, R.: Conserved network motifs allow protein-protein interaction prediction. Bioinformatics 20(18), 3346–3352 (2004)CrossRefGoogle Scholar
  2. 2.
    Artzy-Randrup, Y., Fleishman, S.J., Ben-Tal, N., Stone, L.: Comment on network motifs: Simple building blocks of complex networks and superfamilies of designed and evolved networks. Science 305, 1007c (2004)Google Scholar
  3. 3.
    Bender, E.A.: The asymptotic number of non-negative matrices with given row and column sums. Disc. Appl. Math. 10, 217–223 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bender, E.A., Canfield, E.R.: The asymptotic number of labeled graphs with given degree sequences. J. Comb. Theor. A 24, 296–307 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Berg, J., Lässig, M.: Local graph alignment and motif search in biological networks. PNAS 101(41), 14689–14694 (2004)CrossRefGoogle Scholar
  6. 6.
    Duke, R.A., Lefmann, H., Rödl, V.: A fast approximation algorithm for computing the frequencies of subgraphs in a given graph. SIAM J. Comp. 24(3), 598–620 (1995)zbMATHCrossRefGoogle Scholar
  7. 7.
    Itzkovitz, S., Levitt, R., Kashtan, N., et al.: Coarse-graining and self-dissimilarity of complex networks. Phys. Rev. E 71(016127) (2005)Google Scholar
  8. 8.
    Itzkovitz, S., Milo, R., Kashtan, N., et al.: Subgraphs in random networks. Phys. Rev. E 68(26127) (2003)Google Scholar
  9. 9.
    Kashtan, N., Itzkovitz, S., Milo, R., Alon, U.: Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs. Bioinformatics 20(11), 1746–1758 (2004)CrossRefGoogle Scholar
  10. 10.
    Knuth, D.E.: Estimating the efficiency of backtrack programs. In: Selected papers on Analysis of Algorithms. Stanford Junior University, Palo Alto (2000)Google Scholar
  11. 11.
    Lee, T.I., Rinaldi, N.J., Robert, F., et al.: Transcriptional regulatory networks in Saccharomyces Cerevisiae. Science 298, 799–804 (2002)CrossRefGoogle Scholar
  12. 12.
    McKay, B.D.: Practical graph isomorphism. Congr. Numer. 30, 45–87 (1981)MathSciNetGoogle Scholar
  13. 13.
    Milo, R., Itzkovitz, S., Kashtan, N., et al.: Response to comment on network motifs: Simple building blocks of complex networks and superfamilies of designed and evolved networks. Science 305, 1007d (2004)Google Scholar
  14. 14.
    Milo, R., Itzkovitz, S., Kashtan, N., et al.: Superfamilies of designed and evolved networks. Science 303(5663), 1538–1542 (2004)CrossRefGoogle Scholar
  15. 15.
    Milo, R., Shen-Orr, S.S., Itzkovitz, S., et al.: Network motifs: Simple building blocks of complex networks. Science 298(5594), 824–827 (2002)CrossRefGoogle Scholar
  16. 16.
    Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64(026118) (2001)Google Scholar
  17. 17.
    Ott, S., Hansen, A., Kim, S., Miyano, S.: Superiority of network motifs over optimal networks and an application to the revelation of gene network evolution. Bioinformatics 21(2), 227–238 (2005)CrossRefGoogle Scholar
  18. 18.
    Shen-Orr, S.S., Milo, R., Mangan, S., Alon, U.: Network motifs in the transcriptional regulation network of Escherichia Coli. Nature Gen. 31(1), 64–68 (2002)CrossRefGoogle Scholar
  19. 19.
    Vázquez, A., Dobrin, R., Sergi, D., et al.: The topological relationship between the large-scale attributes and local interaction patterns of complex networks. PNAS 101(52), 17940–17945 (2004)CrossRefGoogle Scholar
  20. 20.
    Vespignani, A.: Evolution thinks modular. Nature Gen 35(2), 118–119 (2003)CrossRefGoogle Scholar
  21. 21.
    Williams, R.J., Martinez, N.D.: Simple rules yield complex food webs. Nature 404, 180–183 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sebastian Wernicke
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations