Graph Summarization With Bounded Error

Abstract

We propose a highly compact two-part representation of a given graph <i>G</i> consisting of a graph summary and a set of corrections. The graph summary is an <i>aggregate</i> graph in which each node corresponds to a set of nodes in <i>G</i>, and each edge represents the edges between all pair of nodes in the two sets. On the other hand, the corrections portion specifies the list of edge-corrections that should be applied to the summary to recreate <i>G</i>. Our representations allow for both lossless and lossy graph compression with bounds on the introduced error. Further, in combination with the MDL principle, they yield highly intuitive coarse-level summaries of the input graph <i>G</i>. We develop algorithms to construct highly compressed graph representations with small sizes and guaranteed accuracy, and validate our approach through an extensive set of experiments with multiple real-life graph data sets. To the best of our knowledge, this is the first work to compute graph summaries using the MDL principle, and use the summaries (along with corrections) to compress graphs with bounded error.