Graph Edit Distance (GED) measures the (dis-)similarity between two given graphs, in terms of the minimum-cost edit sequence that transforms one graph to the other. However, the exact computation of GED is NP-Hard, which has recently motivated the design of neural methods for GED estimation. However, they do not explicitly account for edit operations with different costs. In response, we propose GRAPHEDX, a neural GED estimator that can work with general costs specified for the four edit operations, viz., edge deletion, edge addition, node deletion and node addition. We first present GED as a quadratic assignment problem (QAP) that incorporates these four costs. Then, we represent each graph as a set of node and edge embeddings and use them to design a family of neural set divergence surrogates. We replace the QAP terms corresponding to each operation with their surrogates. Computing such neural set divergence require aligning nodes and edges of the two graphs. We learn these alignments using a Gumbel-Sinkhorn permutation generator, additionally ensuring that the node and edge alignments are consistent with each other. Moreover, these alignments are cognizant of both the presence and absence of edges between node-pairs. Experiments on several datasets, under a variety of edit cost settings, show that GRAPHEDX consistently outperforms state-of-the-art methods and heuristics in terms of prediction error.

翻译：图编辑距离（GED）通过衡量将一个图转换为另一个图所需的最小代价编辑序列来度量两个给定图之间的（不）相似性。然而，GED的精确计算是NP难问题，这促使了近期用于GED估计的神经方法的设计。然而，这些方法未明确考虑具有不同代价的编辑操作。为此，我们提出了GRAPHEDX，一种能够处理为四种编辑操作（即边删除、边添加、节点删除和节点添加）指定通用代价的神经GED估计器。我们首先将GED表述为包含这四种代价的二次分配问题（QAP）。接着，我们将每个图表示为一组节点和边嵌入，并利用它们设计了一系列神经集合散度替代函数。我们将对应于每种操作的QAP项替换为其替代函数。计算此类神经集合散度需要对两个图的节点和边进行对齐。我们使用Gumbel-Sinkhorn置换生成器学习这些对齐，并额外确保节点对齐与边对齐相互一致。此外，这些对齐能够感知节点对之间边的存在与缺失。在多种编辑代价设置下，于多个数据集上的实验表明，GRAPHEDX在预测误差方面持续优于最先进的方法和启发式算法。