Subgraph covers -- An information theoretic approach to motif analysis
in networks
release_b5vnjc2wv5ee3n4dir4gv2ol7q
by
Anatol E. Wegner
2014
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.
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