Enhancing Graph Edit Distance Computation: A Hybrid Method Combining GNN and Graph Structural Features

Graph Edit Distance (GED) computation is a fundamental yet NP-hard problem in graph theory that quantifies the structural dissimilarity between graphs through a series of edit operations. Despite its significance in fields like bioinformatics, cheminformatics, and social network analysis, the computational complexity of exact GED calculation has driven the development of heuristic and approximate methods. This paper proposes a novel approach leveraging Graph Neural Networks to predict GED efficiently. By capturing both local and global graph features through advanced embedding techniques and integrating the Weisfeiler–Lehman graph kernel, our method achieves high accuracy in estimating GED values. Extensive experiments on datasets such as AIDS, Linux, and IMDB demonstrate that our approach outperforms existing methods in terms of mean absolute error (MAE) and computational feasibility. The proposed framework not only enhances the scalability and precision of GED computation, but also provides a robust tool for graph dissimilarity assessments in various application domains.