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Union Subgraph Neural Networks
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Proposes UnionSNN, a GNN that injects a shortest-path-based SVD structural coefficient computed from union subgraphs of edges' 1-hop neighborhoods, proven more expressive than 1-WL and usable as a plugin for MPNNs and Transformers.
Problem
Vanilla MPNNs are bounded by 1-WL because they treat neighbors equally and ignore connectivity among an edge's 1-hop neighborhood; existing substructure methods are either incomplete or computationally expensive.
Approach
Define the union subgraph (induced subgraph on the union of closed neighborhoods of an edge's endpoints), encode it via its all-pairs shortest-path matrix reduced to a scalar by the sum of singular values, and use this as a permutation-invariant structural coefficient weighting neighbor messages in message passing or attention bias.
Key results
- UnionSNN achieves best accuracy on DD (77.00), ENZYMES (68.17), NCI1 (82.34) and NCI109 (81.61) among graph classification baselines, and 74.44 ROC-AUC on OGBG-MOLHIV.
- Plugging the union-subgraph coefficient into GraphSAGE raises ENZYMES accuracy from 52.50 to 58.32 (the paper's reported up-to-11.09% gain).
- UnionGPS reduces ZINC10k MAE from 0.0740 to 0.0681.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use union subgraphs instead of overlap subgraphs (ablation) | UnionSNN · MUTAG | accuracy: 85.70 ± 7.40 -> 87.31 ± 5.29 | Helped |
| use union subgraphs instead of union minus subgraphs (ablation) | UnionSNN · PROTEINS | accuracy: 68.70 ± 3.61 -> 75.02 ± 2.50 | Helped |
| use union subgraphs instead of union minus subgraphs (ablation) | UnionSNN · ENZYMES | accuracy: 65.33 ± 4.58 -> 68.17 ± 5.70 | Helped |
| use union subgraphs instead of union minus subgraphs (ablation) | UnionSNN · DD | accuracy: 74.79 ± 4.63 -> 77.00 ± 2.37 | Helped |
| use union subgraphs instead of union minus subgraphs (ablation) | UnionSNN · NCI1 | accuracy: 80.66 ± 1.90 -> 82.34 ± 1.93 | Helped |
| use union subgraphs instead of union minus subgraphs (ablation) | UnionSNN · NCI109 | accuracy: 78.70 ± 2.48 -> 81.61 ± 1.78 | Helped |
| replace path-matrix descriptor with edge betweenness (ablation) | UnionSNN · graph classification (6 datasets) | accuracy | Hurt |
| replace path-matrix descriptor with node/edge counting (ablation) | UnionSNN · graph classification (6 datasets) | accuracy | Hurt |
| replace path-matrix descriptor with Ricci curvature (ablation) | UnionSNN · graph classification (6 datasets) | accuracy | Hurt |
| replace path-matrix descriptor with Laplacian matrix (ablation) | UnionSNN · graph classification (6 datasets) | accuracy | Mixed |
| encode path matrix by summing singular values rather than summing all elements (ablation) | UnionSNN · graph classification (6 datasets) | accuracy | Mixed |
| encode path matrix by summing singular values rather than using maximum eigenvalue (ablation) | UnionSNN · graph classification (6 datasets) | accuracy | Mixed |
Surprising findings
- On MUTAG, the LapSNN variant (89.39) beats UnionSNN (87.31), and UnionGCN underperforms GCN on DD (69.69 vs 72.16).
Limitations
- Expressiveness limited to cycles up to length 6 since the union subgraph spans only 3 hops.
- Theoretical upper bound of 4-WL; the WL comparison is argued to be only loosely meaningful for local methods.
- Performance is not uniformly best: UnionSNN loses to some baselines on individual datasets (e.g., MUTAG, Tox21).
Experimental setup
Datasets: MUTAG PROTEINS ENZYMES DD FRANKENSTEIN Tox21 NCI1 NCI109 OGBG-MOLHIV OGBG-MOLBBBP ZINC10k ZINC-full
Benchmarks: MUTAG PROTEINS ENZYMES DD FRANKENSTEIN Tox21 NCI1 NCI109 OGBG-MOLHIV OGBG-MOLBBBP ZINC10k ZINC-full
Metrics: accuracy ROC-AUC MAE runtime preprocessing time
Baselines: GCN GIN GraphSAGE GAT GatedGCN 3WL-GNN UGformer MEWISPool CurvGN NestedGIN DropGIN GatedGCN-LSPE
Builds on: GIN GraphSNN Graphormer Ollivier-Ricci curvature
Closest papers by meaning
- Subgraph Neural Networks (NeurIPS 2020 · similarity 0.91)
- Translating Subgraphs to Nodes Makes Simple GNNs Strong and Efficient for Subgraph Representation Learning (ICML 2024 · similarity 0.90)
- A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarsening (NeurIPS 2024 · similarity 0.90)
- Subgraphormer: Unifying Subgraph GNNs and Graph Transformers via Graph Products (ICML 2024 · similarity 0.89)
- Subgraph Invariant Learning Towards Large-Scale Graph Node Classification (AAAI 2025 · similarity 0.88)
- An Efficient Subgraph-Inferring Framework for Large-Scale Heterogeneous Graphs (AAAI 2024 · similarity 0.88)
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