Detecting local network motifs

TL;DR

This paper introduces a new statistical method for detecting local network motifs based on overrepresentation, enabling identification of biologically relevant subgraphs without simulations and providing insights into vertex roles.

Contribution

It proposes a novel local overrepresentation statistic for motif detection that does not require simulations, improving analysis of biological and social networks.

Findings

Successfully detects known biologically relevant motifs

Performs well on both simulated and real data

Provides insights into vertex roles within motifs

Abstract

Studying the topology of so-called real networks, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are built from small functional units called motifs, which can be found by looking for small subgraphs whose numbers of occurrences in the whole network are surprisingly high. In this article, we propose to define motifs through a local overrepresentation in the network and develop a statistic to detect them without relying on simulations. We then illustrate the performance of our procedure on simulated and real data, recovering already known biologically relevant motifs. Moreover, we explain how our method gives some information about the respective roles of the vertices in a motif.