Approximating the Number of Network Motifs

  • Mira Gonen
  • Yuval Shavitt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5427)


World Wide Web, the Internet, coupled biological and chemical systems, neural networks, and social interacting species, are only a few examples of systems composed by a large number of highly interconnected dynamical units. These networks contain characteristic patterns, termed network motifs, which occur far more often than in randomized networks with the same degree sequence. Several algorithms have been suggested for counting or detecting the number of induced or non-induced occurrences of network motifs in the form of trees and bounded treewidth subgraphs of size O(logn), and of size at most 7 for some motifs.

In addition, counting the number of motifs a node is part of was recently suggested as a method to classify nodes in the network. The promise is that the distribution of motifs a node participate in is an indication of its function in the network. Therefore, counting the number of network motifs a node is part of provides a major challenge. However, no such practical algorithm exists.

We present several algorithms with time complexity \(O\left(e^{2k}k\cdot n \cdot |E|\cdot \right.\) \(\left.\log\frac{1}{\delta}/{\epsilon^2}\right)\) that, for the first time, approximate for every vertex the number of non-induced occurrences of the motif the vertex is part of, for k-length cycles, k-length cycles with a chord, and (k − 1)-length paths, where k = O(logn), and for all motifs of size of at most four. In addition, we show algorithms that approximate the total number of non-induced occurrences of these network motifs, when no efficient algorithm exists. Some of our algorithms use the color coding technique.


Time Complexity Undirected Graph Network Motif Simple Path Simple Cycle 
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.


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mira Gonen
    • 1
  • Yuval Shavitt
    • 1
  1. 1.Tel-Aviv UniversityRamat AvivIsrael

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