Graph similarity computation (GSC) aims to quantify the similarity score between two graphs. Although recent GSC methods based on graph neural networks (GNNs) take advantage of intra-graph structures in message passing, few of them fully utilize the structures presented by edges to boost the representation of their connected nodes. Moreover, previous cross-graph node embedding matching lacks the perception of the overall structure of the graph pair, due to the fact that the node representations from GNNs are confined to the intra-graph structure, causing the unreasonable similarity score. Intuitively, the cross-graph structure represented in the assignment graph is helpful to rectify the inappropriate matching. Therefore, we propose a structure-enhanced graph matching network (SEGMN). Equipped with a dual embedding learning module and a structure perception matching module, SEGMN achieves structure enhancement in both embedding learning and cross-graph matching. The dual embedding learning module incorporates adjacent edge representation into each node to achieve a structure-enhanced representation. The structure perception matching module achieves cross-graph structure enhancement through assignment graph convolution. The similarity score of each cross-graph node pair can be rectified by aggregating messages from structurally relevant node pairs. Experimental results on benchmark datasets demonstrate that SEGMN outperforms the state-of-the-art GSC methods in the GED regression task, and the structure perception matching module is plug-and-play, which can further improve the performance of the baselines by up to 25%.

翻译：图相似性计算旨在量化两个图之间的相似度分数。尽管近期基于图神经网络的图相似性计算方法在消息传递中利用了图内结构，但鲜有方法充分利用边所呈现的结构来增强其连接节点的表示。此外，由于图神经网络生成的节点表示受限于图内结构，先前跨图节点嵌入匹配方法缺乏对图对整体结构的感知，导致相似度分数不合理。直观上，由分配图表示的跨图结构有助于修正不恰当的匹配。因此，我们提出了一种结构增强图匹配网络。SEGMN通过配备双重嵌入学习模块和结构感知匹配模块，在嵌入学习和跨图匹配两方面均实现了结构增强。双重嵌入学习模块将邻接边表示融入每个节点，以获得结构增强的表示。结构感知匹配模块通过分配图卷积实现跨图结构增强。每个跨图节点对的相似度分数可通过聚合来自结构相关节点对的消息进行修正。在基准数据集上的实验结果表明，SEGMN在图编辑距离回归任务中优于当前最先进的图相似性计算方法，且结构感知匹配模块具备即插即用特性，可将基线模型的性能提升高达25%。