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DGCLUSTER: A Neural Framework for Attributed Graph Clustering via Modularity Maximization
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Proposes DGCluster, a GCN-based framework that optimizes a differentiable modularity objective via embedding cosine similarity (plus optional auxiliary pairwise-label loss), then clusters embeddings with BIRCH without fixing the number of clusters.
Problem
Attributed graph clustering that maximizes modularity while not requiring the number of clusters in advance and being able to use auxiliary node-level information such as partial labels or known pairwise memberships.
Approach
Replace the binary community membership matrix in modularity with a soft pairwise similarity computed from L2-normalized, positive-space GNN embeddings (cosine = dot product), making modularity differentiable and optimizable with SGD; cluster hard assignments afterward with BIRCH, which does not need k.
Key results
- On Cora, DGCluster (lambda=0.0) reaches modularity 80.7 and conductance 8.4, versus 76.5 and 12.2 for the best prior baseline DMoN.
- With auxiliary label loss (lambda=0.8), DGCluster reaches NMI 62.1 and F1 54.5 on Cora, outperforming DMoN's 48.8 NMI and 48.8 F1.
- Across GNN backbones (GCN, GAT, GIN, GraphSAGE), average modularity stays around 70.5 to 73.8, indicating robustness to the choice of GNN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use auxiliary-information loss with λ increased from 0.0 to 0.8 (ablation) | DGCluster · Cora | NMI: 49.9 -> 62.1 | Helped |
| Use auxiliary-information loss with λ increased from 0.0 to 0.8 (ablation) | DGCluster · Cora | modularity: 80.7 -> 78.6 | Hurt |
| Add auxiliary-information loss (λ=0.2) (ablation) | DGCluster · Citeseer | conductance: 5.5 -> 4.1 | Helped |
| Add auxiliary-information loss (λ=0.2) (ablation) | DGCluster · Citeseer | modularity: 87.2 -> 87.4 | Helped |
| Use GraphSAGE rather than GCN (ablation) | DGCluster · all datasets (average) | conductance: 14.0 -> 9.7 | Helped |
| Use GAT rather than GCN (ablation) | DGCluster · all datasets (average) | modularity: 73.6 -> 73.8 | Helped |
| Use GIN rather than GCN (ablation) | DGCluster · all datasets (average) | modularity: 73.6 -> 72.5 | Hurt |
| Add squared average node-similarity regularization (α=0.5) (ablation) | DGCluster · Cora | modularity: 80.8 -> 80.8 | No clear effect |
| Add squared average node-similarity regularization (α=0.5) (ablation) | DGCluster · Cora | NMI: 43.5 -> 40.3 | Hurt |
Surprising findings
- Adding the auxiliary label loss (higher lambda) lowers modularity while raising NMI, showing a trade-off between structural and label-based objectives.
- The proposed squared average-similarity regularizer has a negligible effect on the main metrics while avoiding trivial single-cluster solutions.
Limitations
- Baseline numbers are taken from the DMoN paper rather than re-run, and the authors fix the optimal lambda per dataset during comparison.
- The F1 score is estimated from 1000 sampled nodes because the exact computation is quadratic.
- Performance on citation networks is only reasonable; the paper reports that DGCluster is not uniformly best, e.g., lower F1 on Citeseer than DMoN.
Experimental setup
Datasets: Cora Citeseer PubMed Amazon PC Amazon Photo Coauthor CS Coauthor PHY
Benchmarks: Cora Citeseer PubMed Amazon PC Amazon Photo Coauthor CS Coauthor PHY
Metrics: modularity conductance NMI F1 score
Baselines: k-means SBM DeepWalk k-means DGI k-means AGC DAEGC SDCN NOCD DiffPool MinCutPool Ortho DMoN
Builds on: DMoN GCN BIRCH Louvain
Closest papers by meaning
- DGCBench: A Deep Graph Clustering Benchmark (NeurIPS 2025 · similarity 0.92)
- Scalable Attribute-Missing Graph Clustering via Neighborhood Differentiation (ICML 2025 · similarity 0.89)
- S3GC: Scalable Self-Supervised Graph Clustering (NeurIPS 2022 · similarity 0.89)
- Every Node Is Different: Dynamically Fusing Self-Supervised Tasks for Attributed Graph Clustering (AAAI 2024 · similarity 0.88)
- THESAURUS: Contrastive Graph Clustering by Swapping Fused Gromov-Wasserstein Couplings (AAAI 2025 · similarity 0.87)
- SURER: Structure-Adaptive Unified Graph Neural Network for Multi-View Clustering (AAAI 2024 · similarity 0.87)
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