Subgraph covers -- An information theoretic approach to motif analysis in networks

TL;DR

This paper introduces an information theoretic method for motif analysis in networks, defining motifs as patterns in subgraph covers that minimize total information, offering an alternative to frequency-based methods.

Contribution

It proposes a novel approach to motif analysis using subgraph covers and minimal total information, connecting to random graph models and providing a heuristic for optimization.

Findings

Effective in identifying motifs in real-world networks

Matches networks with models incorporating motif densities

Heuristic performs well on empirical data

Abstract

Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original network with a statistical null model. In this paper we propose an alternative approach to motif analysis where network motifs are defined to be connectivity patterns that occur in a subgraph cover that represents the network using minimal total information. A subgraph cover is defined to be a set of subgraphs such that every edge of the graph is contained in at least one of the subgraphs in the cover. Some recently introduced random graph models that can incorporate significant densities of motifs have natural formulations in terms of subgraph covers and the presented approach can be used to match networks with such models. To prove the practical value of our approach we also present a heuristic for the resulting NP-hard optimization problem and give results for several real world networks.