Graph Summarization with Quality Guarantees

We study the problem of graph summarization. Given a large graph we aim at producing a concise lossy representation that can be stored in main memory and used to approximately answer queries about the original graph much faster than by using the exact representation. In this paper we study a very natural type of summary: the original set of vertices is partitioned into a small number of super nodes connected by super edges to form a complete weighted graph. The super edge weights are the edge densities between vertices in the corresponding super nodes. The goal is to produce a summary that minimizes the reconstruction error w.r.t. The original graph. By exposing a connection between graph summarization and geometric clustering problems (i.e., k-means and k-median), we develop the first polynomial-time approximation algorithm to compute the best possible summary of a given size.