GEDAN: Learning the Edit Costs for Graph Edit Distance

TL;DR

This paper introduces GEDAN, an end-to-end graph neural network framework that learns context-aware edit costs for graph edit distance, improving interpretability and applicability in complex graph analysis.

Contribution

It presents a novel neural network approach that learns fine-grained, task-specific edit costs for GED, addressing limitations of previous methods assuming uniform costs.

Findings

Outperforms existing approximation methods in accuracy

Produces interpretable graph matchings

Effective in molecular analysis applications

Abstract

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.