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How can we separate structural information from noise in large graphs? Toaddress this fundamental question, we propose a graph summarization approachbased on Szemer\'edi's Regularity Lemma, a well-known result in graph theory,which roughly states that every graph can be approximated by the union of asmall number of random-like bipartite graphs called `regular pairs'. Hence, theRegularity Lemma provides us with a principled way to describe the essentialstructure of large graphs using a small amount of data. Our paper has severalcontributions: (i) We present our summarization algorithm which is able toreveal the main structural patterns in large graphs. (ii) We discuss how to useour summarization framework to efficiently retrieve from a database the top-kgraphs that are most similar to a query graph. (iii) Finally, we evaluate thenoise robustness of our approach in terms of the reconstruction error and theusefulness of the summaries in addressing the graph search task.

Separating Structure from Noise in Large Graphs Using the Regularity Lemma