  Graph similarity computation aims to predict a similarity score between one
pair of graphs to facilitate downstream applications, such as finding the most
similar chemical compounds similar to a query compound or Fewshot 3D Action
Recognition. Recently, some graph similarity computation models based on neural
networks have been proposed, which are either based on graph-level interaction
or node-level comparison. However, when the number of nodes in the graph
increases, it will inevitably bring about reduced representation ability or
high computation cost. Motivated by this observation, we propose a graph
partitioning and graph neural network-based model, called PSimGNN, to
effectively resolve this issue. Specifically, each of the input graphs is
partitioned into a set of subgraphs to extract the local structural features
directly. Next, a novel graph neural network with an attention mechanism is
designed to map each subgraph into an embedding vector. Some of these subgraph
pairs are automatically selected for node-level comparison to supplement the
subgraph-level embedding with fine-grained information. Finally, coarse-grained
interaction information among subgraphs and fine-grained comparison information
among nodes in different subgraphs are integrated to predict the final
similarity score. Experimental results on graph datasets with different graph
sizes demonstrate that PSimGNN outperforms state-of-the-art methods in graph
similarity computation tasks using approximate Graph Edit Distance (GED) as the
graph similarity metric.
