Graph Summarization for Preserving Spectral Characteristics

How does the graph change if we summarize it by merging nodes? How can we summarize the graph while preserving its spectral characteristics? Graph summarization aims to present a graph in a compact summary graph form while keeping its important structural information. Existing methods primarily focus on preserving the adjacency matrix. In contrast, spectral graph theory provides a powerful tool to describe the characteristics of a graph. In this paper, we propose a novel graph summarization method that preserves the spectral characteristics, including spectral moments and heat traces. We analyze the change of the spectral characteristics after summarization and design a simple yet effective summarization method based on agglomerative clustering. Our approach is extensively evaluated on real-world datasets. The experimental results show that our method excels in preserving the spectral characteristics and obtains better performance on the subsequent graph classification task.