Node Embedding Preserving Graph Summarization

Houquan Zhou, Shenghua Liu, Huawei Shen, Xueqi Cheng

Abstract: Graph summarization is a useful tool for analyzing large-scale graphs. Some works tried to preserve original node embeddings encoding rich structural information of nodes on the summary graph. However, their algorithms are designed heuristically and not theoretically guaranteed. In this article, we theoretically study the problem of preserving node embeddings on summary graph. We prove that three matrix-factorization-based node embedding methods of the original graph can be approximated by that of the summary graph, and we propose a novel graph summarization method, named HCSumm, based on this analysis. Extensive experiments are performed on real-world datasets to evaluate the effectiveness of our proposed method. The experimental results show that our method outperforms the state-of-the-art methods in preserving node embeddings.