Summarizing graphs using the configuration model

Abstract: Given a large graph, how can we summarize it with fewer nodes and edges while maintaining its key properties, such as spectral property? Although graphs play more and more important roles in many real-world applications, the growth of their size presents great challenges to graph analysis. As a solution, graph summarization, which aims to find a compact representation that preserves the important properties of a given graph, has received much attention, and numerous algorithms have been developed for it. However, most of the algorithms adopt the uniform reconstruction scheme, which is based on an unrealistic assumption that edges are uniformly distributed. In this work, we propose a novel and realistic reconstruction scheme, which preserves the degree of nodes, and we develop an efficient graph summarization algorithm called DPGS based on the Minimum Description Length principle. We theoretically analyze the difference between the original and summary graphs from a spectral perspective, and we perform extensive experiments on multiple real-world datasets. The results show that DPGS yields compact representation that preserves the essential properties of the original graph.