Separating Structure from Noise in Large Graphs Using the Regularity Lemma. (February 2020) - Fiorucci, Marco; Pelosin, Francesco; Pelillo, Marcello
Highlights: Provides a summarization algorithm based on the Regularity Lemma, which is able to separate structural information from noise in large graphs. Discusses how to use our summarization framework to efficiently retrieve from a database the top-k graphs that are most similar to a query graph. Successfully validates the proposed framework both on synthetic and real-world networks showing that our algorithm surpasses the state-of-the-art in terms of noise robustness. Abstract: How can we separate structural information from noise in large graphs? To address this fundamental question, we propose a graph summarization approach based on Szemerédi's Regularity Lemma, a well-known result in graph theory, which roughly states that every graph can be approximated by the union of a small number of random-like bipartite graphs called "regular pairs". Hence, the Regularity Lemma provides us with a principled way to describe the essential structure of large graphs using a small amount of data. Our paper has several contributions: (i) We present our summarization algorithm which is able to reveal the main structural patterns in large graphs. (ii) We discuss how to use our summarization framework to efficiently retrieve from a database the top- k graphs that are most similar to a query graph. (iii) Finally, we evaluate the noise robustness of our approach in terms of the reconstruction error and the usefulness of the summaries in addressing the graph search task.