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CoRe-GD: A Hierarchical Framework for Scalable Graph Visualization with GNNs
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CoRe-GD is a scalable GNN graph drawing framework that optimizes stress via a coarsening hierarchy, recurrent layout refinement, and positional rewiring from intermediate decoded positions.
Problem
Stress-based graph drawing is computationally hard and usually solved by heuristics; existing learned graph drawing models do not scale to large graphs because message passing is local or fully connected (quadratic).
Approach
Combine a multilevel graph coarsening hierarchy (global-first layout, uncoarsening) with a recurrent GNN that passes latent embeddings and rewires the graph using KNN over intermediate decoded positions, plus beacon-distance features and a replay buffer of latent embeddings for training deep recurrent GNNs with scale-invariant stress loss.
Key results
- On Rome, CoRe-GD achieves mean scale-invariant stress 233.17 ± 0.13, the best among compared methods (vs. (sgd)^2 233.49 and DeepGD 235.22).
- On the SuiteSparse subset, CoRe-GD with coarsening reaches stress 42639 ± 313, close to (sgd)^2 at 42435 ± 149 and better than neato, sfdp, and PivotMDS; without coarsening it reaches 45573.
- CoRe-GD scales to graphs of up to 1,000 nodes in training and runs on graphs up to 25,000 nodes, while DeepGD was limited to 5,000 nodes by GPU memory.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use CoRe-GD instead of the strongest listed baseline | Graph drawing methods · Rome | stress: 233.49 $\pm$ 0.22 -> 233.17 $\pm$ 0.13 | Helped |
| use CoRe-GD instead of the strongest listed baseline | Graph drawing methods · ZINC | stress: 5.14 $\pm$ 0.01 -> 5.11 $\pm$ 0.02 | Helped |
| use CoRe-GD instead of the strongest listed baseline | Graph drawing methods · MNIST | stress: 129.19 $\pm$ 0.00 -> 129.10 $\pm$ 0.02 | Helped |
| use CoRe-GD instead of the strongest listed baseline | Graph drawing methods · CIFAR10 | stress: 262.52 $\pm$ 0.00 -> 262.68 $\pm$ 0.08 | Hurt |
| use CoRe-GD instead of the strongest listed baseline | Graph drawing methods · PATTERN | stress: 3080.70 $\pm$ 0.24 -> 3067.02 $\pm$ 0.79 | Helped |
| use CoRe-GD instead of the strongest listed baseline | Graph drawing methods · CLUSTER | stress: 2838.13 $\pm$ 0.08 -> 2827.81 $\pm$ 0.36 | Helped |
| add the GRU convolution instead of using GIN convolution (ablation) | CoRe-GD · Rome | stress: 238.53 $\pm$ 1.43 -> 233.17 $\pm$ 0.13 | Helped |
| add the GRU convolution instead of using GAT convolution (ablation) | CoRe-GD · Rome | stress: 270.83 $\pm$ 8.45 -> 233.17 $\pm$ 0.13 | Helped |
| add beacon distance features (ablation) | CoRe-GD · Rome | stress: 233.39 $\pm$ 0.30 -> 233.17 $\pm$ 0.13 | No clear effect |
| add Laplacian positional encodings (ablation) | CoRe-GD · Rome | stress: 234.65 $\pm$ 0.33 -> 233.17 $\pm$ 0.13 | Helped |
| add random node features (ablation) | CoRe-GD · Rome | stress: 233.24 $\pm$ 0.17 -> 233.17 $\pm$ 0.13 | No clear effect |
| add positional rewiring (ablation) | CoRe-GD · Rome | stress: 236.38 $\pm$ 0.12 -> 233.17 $\pm$ 0.13 | Helped |
Surprising findings
- CoRe-GD outperforms all other methods on all datasets except CIFAR10, where (sgd)^2 is slightly better.
- Training DeepGD on graphs beyond 200 nodes ran into GPU memory problems, and DeepGD becomes unstable under out-of-distribution graph sizes.
Limitations
- Delaunay rewiring is slow in practice because triangulation runs on CPU; radius graphs are sensitive to graph size and threshold.
- Hyperparameters were tuned by line search rather than full grid search due to computational constraints.
- Performance degrades for graphs beyond the training size distribution.
Experimental setup
Datasets: Rome ZINC MNIST CIFAR10 PATTERN CLUSTER SuiteSparse matrix collection Delaunay triangulations of random point clouds
Benchmarks: Rome ZINC MNIST CIFAR10 PATTERN CLUSTER SuiteSparse subset Delaunay random graphs (scaling)
Metrics: scale-invariant stress normalized scale-invariant stress runtime
Baselines: PivotMDS neato sfdp (sgd)^2 (DNN)^2 DeepGD
Builds on: DeepGD maxent-stress GRU-based recurrent GNN spectral-preserving coarsening Pivot MDS
Closest papers by meaning
- Adapting to Evolving Graphs: A Scalable Framework for Dynamic Coarsening (ICML 2026 · similarity 0.85)
- A Flexible, Equivariant Framework for Subgraph GNNs via Graph Products and Graph Coarsening (NeurIPS 2024 · similarity 0.84)
- Generative Graph Pattern Machine (NeurIPS 2025 · similarity 0.83)
- Graph Coarsening via Supervised Granular-Ball for Scalable Graph Neural Network Training (AAAI 2025 · similarity 0.83)
- The Intelligible and Effective Graph Neural Additive Network (NeurIPS 2024 · similarity 0.83)
- WatE: A Wasserstein t-distributed Embedding Method for Information-enriched Graph Visualization (AAAI 2025 · similarity 0.83)
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