Abstract
A motif in a network is a connected graph that occurs significantly more frequently as an induced subgraph than would be expected in a similar randomized network. By virtue of being atypical, it is thought that motifs might play a more important role than arbitrary subgraphs. Recently, a flurry of advances in the study of network motifs has created demand for faster computational means for identifying motifs in increasingly larger networks. Motif detection is typically performed by enumerating subgraphs in an input network and in an ensemble of comparison networks; this poses a significant computational problem. Classifying the subgraphs encountered, for instance, is typically performed using a graph canonical labeling package, such as Nauty, and will typically be called billions of times. In this article, we describe an implementation of a network motif detection package, which we call NetMODE. NetMODE can only perform motif detection for [Formula: see text]-node subgraphs when [Formula: see text], but does so without the use of Nauty. To avoid using Nauty, NetMODE has an initial pretreatment phase, where [Formula: see text]-node graph data is stored in memory ([Formula: see text]). For [Formula: see text] we take a novel approach, which relates to the Reconstruction Conjecture for directed graphs. We find that NetMODE can perform up to around [Formula: see text] times faster than its predecessors when [Formula: see text] and up to around [Formula: see text] times faster when [Formula: see text] (the exact improvement varies considerably). NetMODE also (a) includes a method for generating comparison graphs uniformly at random, (b) can interface with external packages (e.g. R), and (c) can utilize multi-core architectures. NetMODE is available from netmode.sf.net.
Highlights
A network motif in a network G is a connected graph H that occurs significantly more frequently as an induced subgraph than would be expected in a ‘‘similar’’ random network
The number of similar graphs generated for comparison is always 1000, and we use zero burnin
In the power network tested in [15], we find that S amounts to more than 47% and 12% of the total run-time in FanMod, when performing a 3-node and 4-node subgraph census, respectively
Summary
A network motif in a network G is a connected graph H that occurs significantly more frequently as an induced subgraph than would be expected in a ‘‘similar’’ random network. The term ‘‘network motif’’ was coined by [1,2], who discovered that they occur in several biological and artificial networks. Network motifs have been found in a vast range of networks, and, in some cases, have been identified as functionally important. One prominent example is the 3-node feed-forward loop in the E. coli transcription factor network [3]. See [4,5]. See Supporting Information S1 for an introduction to the graph theory concepts used in this paper
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