Bioinformatics Advance Access originally published online on March 4, 2004
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Bioinformatics 20(11) © Oxford University Press 2004; all rights reserved.
Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs
1 Department of Molecular Cell biology, 2 Department of Physics of Complex Systems and 3 Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Received on July 22, 2003; revised on December 2, 2003; accepted on January 8, 2004
Advance Access Publication March 4, 2004
Summary: Biological and engineered networks have recently been shown to display network motifs: a small set of characteristic patterns that occur much more frequently than in randomized networks with the same degree sequence. Network motifs were demonstrated to play key information processing roles in biological regulation networks. Existing algorithms for detecting network motifs act by exhaustively enumerating all subgraphs with a given number of nodes in the network. The runtime of such algorithms increases strongly with network size. Here, we present a novel algorithm that allows estimation of subgraph concentrations and detection of network motifs at a runtime that is asymptotically independent of the network size. This algorithm is based on random sampling of subgraphs. Network motifs are detected with a surprisingly small number of samples in a wide variety of networks. Our method can be applied to estimate the concentrations of larger subgraphs in larger networks than was previously possible with exhaustive enumeration algorithms. We present results for high-order motifs in several biological networks and discuss their possible functions.
Availability: A software tool for estimating subgraph concentrations and detecting network motifs (mfinder 1.1) and further information is available at http://www.weizmann.ac.il/mcb/UriAlon/
Contact: urialon{at}weizmann.ac.il
* To whom correspondence should be addressed.
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