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Many real world networks contain a statistically surprising number of certainsubgraphs, called network motifs. In the prevalent approach to motif analysis,network motifs are detected by comparing subgraph frequencies in the originalnetwork with a statistical null model. In this paper we propose an alternativeapproach to motif analysis where network motifs are defined to be connectivitypatterns that occur in a subgraph cover that represents the network usingminimal total information. A subgraph cover is defined to be a set of subgraphssuch that every edge of the graph is contained in at least one of the subgraphsin the cover. Some recently introduced random graph models that can incorporatesignificant densities of motifs have natural formulations in terms of subgraphcovers and the presented approach can be used to match networks with suchmodels. To prove the practical value of our approach we also present aheuristic for the resulting NP-hard optimization problem and give results forseveral real world networks.

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