Biological and engineered networks have recently been shown to display network motifs: a small set of characteristic patterns which 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 full enumeration 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 run time 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 full 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 2.0) and further information is available at:
Similarly, Kashtan et al. REF used a modified random link selection for estimation and detection of network motifs and also other subgraphs in large networks.
Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs
Bioinformatics
Computer Science Medicine