  Graph similarity measurement, which computes the distance/similarity between
two graphs, arises in various graph-related tasks. Recent learning-based
methods lack interpretability, as they directly transform interaction
information between two graphs into one hidden vector and then map it to
similarity. To cope with this problem, this study proposes a more interpretable
end-to-end paradigm for graph similarity learning, named Similarity Computation
via Maximum Common Subgraph Inference (INFMCS). Our critical insight into
INFMCS is the strong correlation between similarity score and Maximum Common
Subgraph (MCS). We implicitly infer MCS to obtain the normalized MCS size, with
the supervision information being only the similarity score during training. To
capture more global information, we also stack some vanilla transformer encoder
layers with graph convolution layers and propose a novel permutation-invariant
node Positional Encoding. The entire model is quite simple yet effective.
Comprehensive experiments demonstrate that INFMCS consistently outperforms
state-of-the-art baselines for graph-graph classification and regression tasks.
Ablation experiments verify the effectiveness of the proposed computation
paradigm and other components. Also, visualization and statistics of results
reveal the interpretability of INFMCS.
