Learning Graph Edit Distance Via Node Matching Patterns.

Graph edit distance (GED) is a general and versatile measure of graph similarity. Many combinatorial algorithms have been proposed for computing exact GED, but they suffer from the high computational cost due to the NP-hardness of GED computation. To address this challenge, approximate GED computation techniques have been extensively studied. These techniques are generally twofold: early work is based on combinatorial algorithms that restrict search space for efficient computation, while more recent approaches employ machine learning techniques to estimate GED. Although learning-based approaches generally achieve higher estimation accuracy than combinatorial approximations, they often rely on smoothed node embeddings to model node-to-node interactions, which may limit their ability to capture fine-grained structural differences. To alleviate this limitation, we exploit the insight that sequential variations in node interactions across GNN layers exhibit informative patterns. In this paper, we design a novel neural model, Grasp, that learns to extract and leverage these patterns to predict pairwise node matching probabilities and their associated costs. By aggregating these estimates from the perspectives of both input graphs, Grasp effectively and accurately computes an approximate GED. Experimental results on real-world datasets demonstrate that Grasp significantly improves estimation accuracy over existing approximate methods.