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.
Highlights
Many complex systems can be modeled as networks where vertices represent interacting elements and edges interactions between them
We introduce an alternative approach to motif analysis that is based on using subgraph covers as representations of graphs
We introduced an alternative approach to motif analysis in networks that is based on finding a subgraph cover of the network that represents it using minimal total information
Summary
Many complex systems can be modeled as networks where vertices represent interacting elements and edges interactions between them. A large number of real-world networks has been found to contain a statistically surprising number of certain small connectivity patterns called network motifs [1]. Network motifs, which are commonly referred to as basic building blocks of networks, are thought to play an important role in the structural and functional organization of complex networks. The prevalent approach to motif analysis is due to Milo et al [1] and is based on comparing the subgraph frequencies of the original network with a statistical null model that preserves some features of the original network. Motifs for which the frequencies significantly deviate from the null model are classified as network motifs. In their original paper, Milo et al
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