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How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the ‘importance’ of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a ‘vocabulary’ of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop VOG, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph.
Koutra et al. (Mon,) studied this question.