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Graph similarity computation aims to predict a similarity score between onepair of graphs to facilitate downstream applications, such as finding the mostsimilar chemical compounds similar to a query compound or Fewshot 3D ActionRecognition. Recently, some graph similarity computation models based on neuralnetworks have been proposed, which are either based on graph-level interactionor node-level comparison. However, when the number of nodes in the graphincreases, it will inevitably bring about reduced representation ability orhigh computation cost. Motivated by this observation, we propose a graphpartitioning and graph neural network-based model, called PSimGNN, toeffectively resolve this issue. Specifically, each of the input graphs ispartitioned into a set of subgraphs to extract the local structural featuresdirectly. Next, a novel graph neural network with an attention mechanism isdesigned to map each subgraph into an embedding vector. Some of these subgraphpairs are automatically selected for node-level comparison to supplement thesubgraph-level embedding with fine-grained information. Finally, coarse-grainedinteraction information among subgraphs and fine-grained comparison informationamong nodes in different subgraphs are integrated to predict the finalsimilarity score. Experimental results on graph datasets with different graphsizes demonstrate that PSimGNN outperforms state-of-the-art methods in graphsimilarity computation tasks using approximate Graph Edit Distance (GED) as thegraph similarity metric.

Graph Partitioning and Graph Neural Network based Hierarchical Graph Matching for Graph Similarity Computation