Network motifs detection using random networks with prescribed subgraph frequencies

In order to detect network motifs we need to evaluate the exceptionality of subgraphs in a given network. This is usually done by comparing subgraph frequencies on both the original and an ensemble of random networks keeping certain structural properties. The classical null model implies preserving the degree sequence. In this paper our focus is on a richer model that approximately fixes the frequency of subgraphs of size K - 1 to compute motifs of size K. We propose a method for generating random graphs under this model, and we provide algorithms for its efficient computation. We show empirical results of our proposed methodology on neurobiological networks, showcasing its efficiency and its differences when comparing to the traditional null model.