# SimGNN: A Neural Network Approach to Fast Graph Similarity Computation

arXiv: https://arxiv.org/abs/1808.05689 · HTML: https://mlsanity.com/paper/1808.05689/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2018.

## Built on by (most cited first, 30 of 90)

- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
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- [GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection](https://mlsanity.com/paper/2211.04208/) (2022)
- [GREED: A Neural Framework for Learning Graph Distance Functions](https://mlsanity.com/paper/2112.13143/) (2021)
- [A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2106.04927/) (2021)
- [Efficient Graph Similarity Computation with Alignment Regularization](https://mlsanity.com/paper/2406.14929/) (2024)
- [Multilingual Knowledge Graph Completion with Self-Supervised Adaptive Graph Alignment](https://mlsanity.com/paper/2203.14987/) (2022)
- [Conditional Graph Information Bottleneck for Molecular Relational Learning](https://mlsanity.com/paper/2305.01520/) (2023)
- [FAITH: Few-Shot Graph Classification with Hierarchical Task Graphs](https://mlsanity.com/paper/2205.02435/) (2022)
- [Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learning](https://mlsanity.com/paper/2104.05960/) (2021)
- [Shift-Robust Molecular Relational Learning with Causal Substructure](https://mlsanity.com/paper/2305.18451/) (2023)
- [Towards Data-centric Graph Machine Learning: Review and Outlook](https://mlsanity.com/paper/2309.10979/) (2023)
- [Towards Prototype-Based Self-Explainable Graph Neural Network](https://mlsanity.com/paper/2210.01974/) (2022)
- [Zero-shot Item-based Recommendation via Multi-task Product Knowledge Graph Pre-Training](https://mlsanity.com/paper/2305.07633/) (2023)
- [Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More](https://mlsanity.com/paper/2107.06876/) (2021)
- [MM-GNN: Mix-Moment Graph Neural Network towards Modeling Neighborhood Feature Distribution](https://mlsanity.com/paper/2208.07012/) (2022)
- [Graph Edit Distance with General Costs Using Neural Set Divergence](https://mlsanity.com/paper/2409.17687/) (2024)
- [SG-PGM: Partial Graph Matching Network with Semantic Geometric Fusion for 3D Scene Graph Alignment and Its Downstream Tasks](https://mlsanity.com/paper/2403.19474/) (2024)
- [Neural Graph Matching based Collaborative Filtering](https://mlsanity.com/paper/2105.04067/) (2021)
- [STAR: Sparse Transformer-based Action Recognition](https://mlsanity.com/paper/2107.07089/) (2021)
- [CGMN: A Contrastive Graph Matching Network for Self-Supervised Graph Similarity Learning](https://mlsanity.com/paper/2205.15083/) (2022)
- [More Interpretable Graph Similarity Computation via Maximum Common Subgraph Inference](https://mlsanity.com/paper/2208.04580/) (2022)
- [Maximum Common Subgraph Guided Graph Retrieval: Late and Early Interaction Networks](https://mlsanity.com/paper/2210.11020/) (2022)
- [The quest for the GRAph Level autoEncoder (GRALE)](https://mlsanity.com/paper/2505.22109/) (2025)
- [Meta-Learning with Graph Neural Networks: Methods and Applications](https://mlsanity.com/paper/2103.00137/) (2021)
- [CAD 3D Model classification by Graph Neural Networks: A new approach based on STEP format](https://mlsanity.com/paper/2210.16815/) (2022)
- [Computing Approximate Graph Edit Distance via Optimal Transport](https://mlsanity.com/paper/2412.18857/) (2024)
- [Graph Neural Networks for Databases: A Survey](https://mlsanity.com/paper/2502.12908/) (2025)
- [Sub-GMN: The Neural Subgraph Matching Network Model](https://mlsanity.com/paper/2104.00186/) (2021)

## Abstract (arXiv)

Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common Subgraph (MCS), is the core operation of graph similarity search and many other applications, but very costly to compute in practice. Inspired by the recent success of neural network approaches to several graph applications, such as node or graph classification, we propose a novel neural network based approach to address this classic yet challenging graph problem, aiming to alleviate the computational burden while preserving a good performance. The proposed approach, called SimGNN, combines two strategies. First, we design a learnable embedding function that maps every graph into a vector, which provides a global summary of a graph. A novel attention mechanism is proposed to emphasize the important nodes with respect to a specific similarity metric. Second, we design a pairwise node comparison method to supplement the graph-level embeddings with fine-grained node-level information. Our model achieves better generalization on unseen graphs, and in the worst case runs in quadratic time with respect to the number of nodes in two graphs. Taking GED computation as an example, experimental results on three real graph datasets demonstrate the effectiveness and efficiency of our approach. Specifically, our model achieves smaller error rate and great time reduction compared against a series of baselines, including several approximation algorithms on GED computation, and many existing graph neural network based models. To the best of our knowledge, we are among the first to adopt neural networks to explicitly model the similarity between two graphs, and provide a new direction for future research on graph similarity computation and graph similarity search.