GEDAN: Learning the Edit Costs for Graph Edit Distance

Graph Edit Distance (GED) is defined as the minimum cost transformation of one graph into another and is a widely adopted metric for measuring the dissimilarity between graphs. The major problem of GED is that its computation is NP-hard, which has in turn led to the development of various approximation methods, including approaches based on neural networks (NN). However, most NN methods assume a unit cost for edit operations -- a restrictive and often unrealistic simplification, since topological and functional distances rarely coincide in real-world data. In this paper, we propose a fully end-to-end Graph Neural Network framework for learning the edit costs for GED, at a fine-grained level, aligning topological and task-specific similarity. Our method combines an unsupervised self-organizing mechanism for GED approximation with a Generalized Additive Model that flexibly learns contextualized edit costs. Experiments demonstrate that our approach overcomes the limitations of non-end-to-end methods, yielding directly interpretable graph matchings, uncovering meaningful structures in complex graphs, and showing strong applicability to domains such as molecular analysis.