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HiGen: Hierarchical Graph Generative Networks
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Proposes HiGen, a hierarchical coarse-to-fine graph generative model that generates Louvain-partitioned communities in parallel and then predicts cross-community bipartite edges, using a multinomial/stick-breaking factorization for integer edge weights.
Problem
Generating realistic generic graphs while capturing their hierarchical community structure, with scalability to large graphs and integer-valued (multi)edge weights, which existing autoregressive, GAN, and diffusion generators handle poorly.
Approach
Model graph generation as a recursive coarse-to-fine process over Louvain hierarchies: communities at each level are generated in parallel conditioned on parent super-nodes, then cross-community bipartite edges are predicted by a separate GraphGPS-based network; edge weights are modeled via a multinomial factorized into binomial/multinomial stick-breaking steps.
Key results
- On Ego, HiGen achieves FD 5.24 versus 15.76 for the best prior baseline EDGE, and Clus. MMD 0.0031 versus 0.0092 for DiGress.
- On Enzyme, HiGen reaches Clus. 0.038 and Orbit 7.2e-4, best among compared models including GraphARM (0.054 Clus.).
- On Protein, HiGen reports Deg. 0.0012 and Spec. 0.0025, improving over SPECTRE's 0.0052 Spec. MMD; the authors claim state-of-the-art on all benchmarks.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use mixture of multinomial distributions for leaf-edge output instead of HiGen's mixture of Bernoulli (ablation) | HiGen · SBM | orbit MMD: 0.0352 -> 0.0604 | Hurt |
| use mixture of multinomial distributions for leaf-edge output instead of HiGen's mixture of Bernoulli (ablation) | HiGen · Protein | clustering MMD: 0.0435 -> 0.109 | Hurt |
| use mixture of multinomial distributions for leaf-edge output instead of HiGen's mixture of Bernoulli (ablation) | HiGen · Enzyme | clustering MMD: 0.038 -> 0.157 | Hurt |
| use mixture of multinomial distributions for leaf-edge output instead of HiGen's mixture of Bernoulli (ablation) | HiGen · Ego | Frechet Distance: 5.24 -> 12.2 | Hurt |
| use mixture of multinomial distributions for leaf-edge output instead of HiGen's mixture of Bernoulli (ablation) | HiGen · Ego | GNN RBF: 0.0454 -> 0.0420 | Helped |
| use mixture of multinomial distributions for leaf-edge output instead of HiGen's mixture of Bernoulli (ablation) | HiGen · SBM | degree MMD: 0.0019 -> 0.0017 | Mixed |
| use mixture of multinomial distributions for leaf-edge output instead of HiGen's mixture of Bernoulli (ablation) | HiGen · Protein | degree MMD: 0.0012 -> 0.0041 | Hurt |
| use hierarchical HiGen rather than DiGress | graph generation · SBM | clustering MMD: 0.0498 -> 0.0498 | No clear effect |
| use hierarchical HiGen rather than SPECTRE | graph generation · Protein | orbit MMD: 0.0267 -> 0.0234 | Helped |
| use hierarchical HiGen rather than DiGress | graph generation · Enzyme | orbit MMD: 0.002 -> 7.2e-4 | Helped |
| use hierarchical HiGen rather than DiGress | graph generation · Ego | clustering MMD: 0.0092 -> 0.0031 | Helped |
Surprising findings
- The paper notes that for the point cloud dataset, the full augmented bipartite graph causes out-of-memory, so sub-graph sampling of bipartites is used; the authors argue edge independence matters less for sparse inter-community edges.
Limitations
- Default partitioning uses Louvain with a fixed depth L=2, and the generated graph structure depends on the choice of coarsening algorithm.
- Leaf-level edges are binary and the paper uses a multi-hot/Bernoulli output, so the cardinality potential extension is left for future work.
- Full bipartite generation runs out of memory on large graphs, requiring a sub-graph sampling variant (HiGen-s).
Experimental setup
Datasets: Stochastic Block Model (SBM) Protein Enzyme Ego (CiteSeer 3-hop) Point Cloud
Benchmarks: SBM Protein Enzyme Ego Point Cloud
Metrics: MMD degree distribution MMD clustering coefficient MMD orbit count MMD spectrum GNN RBF MMD Frechet Distance
Baselines: GraphRNN GRAN SPECTRE DiGress GDSS GraphARM EDGE DiscDDPM
Builds on: GRAN GraphGPS GraphRNN Louvain algorithm DeepGMG
Closest papers by meaning
- Towards Addressing Frontiers in Graph Generation (AAAI 2025 · similarity 0.90)
- On the Role of Edge Dependency in Graph Generative Models (ICML 2024 · similarity 0.90)
- Efficient and Scalable Graph Generation through Iterative Local Expansion (ICLR 2024 · similarity 0.88)
- Generative Graph Pattern Machine (NeurIPS 2025 · similarity 0.88)
- HYGENE: A Diffusion-Based Hypergraph Generation Method (AAAI 2025 · similarity 0.87)
- SBGD: Improving Graph Diffusion Generative Model via Stochastic Block Diffusion (ICML 2025 · similarity 0.87)
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