Graph Edit Distance (GED) is a widely used measure of graph similarity, valued for its flexibility in encoding domain knowledge through operation costs. However, existing learning-based approximation methods follow a modeling paradigm that decouples local candidate match selection from both operation costs and global dependencies between matches. This decoupling undermines their ability to capture the intrinsic flexibility of GED and often forces them to rely on costly iterative refinement to obtain accurate alignments. In this work, we revisit the formulation of GED and revise the prevailing paradigm, and propose Graph Edit Network (GEN), an implementation of the revised formulation that tightly integrates cost-aware expense estimation with globally guided one-step alignment. Specifically, GEN incorporates operation costs into node matching expenses estimation, ensuring match decisions respect the specified cost setting. Furthermore, GEN models match dependencies within and across graphs, capturing each match's impact on the overall alignment. These designs enable accurate GED approximation without iterative refinement. Extensive experiments on real-world and synthetic benchmarks demonstrate that GEN achieves up to a 37.8% reduction in GED predictive errors, while increasing inference throughput by up to 414x. These results highlight GEN's practical efficiency and the effectiveness of the revision. Beyond this implementation, our revision provides a principled framework for advancing learning-based GED approximation.

翻译：图编辑距离（GED）是一种广泛使用的图相似度度量方法，其优势在于能够通过操作成本灵活地编码领域知识。然而，现有的基于学习的近似方法遵循一种建模范式，该范式将局部候选匹配选择与操作成本以及匹配间的全局依赖关系解耦。这种解耦削弱了它们捕捉GED内在灵活性的能力，并常常迫使它们依赖昂贵的迭代优化来获得准确的对齐。在本工作中，我们重新审视GED的公式化表述，修正了主流范式，并提出了图编辑网络（GEN），作为修正后公式的一个实现，它将成本感知的匹配开销估计与全局引导的一步对齐紧密集成。具体而言，GEN将操作成本纳入节点匹配开销估计，确保匹配决策尊重指定的成本设置。此外，GEN对图内和图间的匹配依赖关系进行建模，捕捉每个匹配对整体对齐的影响。这些设计使得无需迭代优化即可实现准确的GED近似。在真实世界和合成基准数据集上进行的大量实验表明，GEN将GED预测误差降低了高达37.8%，同时将推理吞吐量提升了高达414倍。这些结果突显了GEN的实用效率以及本次修正的有效性。除了这一具体实现，我们的修正为推进基于学习的GED近似提供了一个原则性框架。