Network motifs come in sets: correlations in the randomization process

TL;DR

This paper reveals that the process of randomizing networks for motif detection introduces correlated changes in subgraph counts, affecting the independence of motif identification.

Contribution

It demonstrates the correlated effects of randomization algorithms on subgraph counts and introduces an information-theoretic method to identify such correlations.

Findings

Randomization algorithms induce correlated changes in subgraph counts.

Correlations among motifs can be interpreted and quantified.

An information-theoretic tool for detecting subgraph correlations is proposed.

Abstract

The identification of motifs--subgraphs that appear significantly more often in a particular network than in an ensemble of randomized networks--has become a ubiquitous method for uncovering potentially important subunits within networks drawn from a wide variety of fields. We find that the most common algorithms used to generate the ensemble from the real network change subgraph counts in a highly correlated manner, so that one subgraph's status as a motif may not be independent from the statuses of the other subgraphs. We demonstrate this effect for the problem of 3- and 4-node motif identification in the transcriptional regulatory networks of E. coli and S. cerevisiae in which randomized networks are generated via an edge-swapping algorithm (Milo et al., Science 298:824, 2002). We show that correlations among 3-node subgraphs are easily interpreted, and we present an information-theoretic tool that may be used to identify correlations among subgraphs of any size.