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What Is Missing For Graph Homophily? Disentangling Graph Homophily For Graph Neural Networks
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Disentangles graph homophily into label, structural, and feature components, proposes the CSBM-3H generative model and a composite metric Tri-Hom that correlates better with GNN performance than 17 existing homophily metrics on 31 datasets.
Problem
Conventional homophily metrics (edge, node homophily) that measure label consistency across topology correlate poorly with GNN performance, and it is unclear how homophily affects GNNs.
Approach
Disentangle graph homophily into label, structural (neighbor-distribution consistency within classes), and feature (feature dependency across topology via a graph diffusion model) homophily; generate graphs with a CSBM-3H model controlling all three; derive a closed-form composite metric Tri-Hom from node distinguishability.
Key results
- Tri-Hom J^G_h achieves the highest Pearson correlation with GCN performance (0.6650) and the highest average rank (1.50) among 20+ metrics across the four models.
- Tri-Hom J^G_h correlates with GAT performance at 0.6731, versus 0.5344 for edge homophily and 0.5832 for aggregation homophily.
- Theory shows the worst GNN performance occurs at label homophily h_L = 1/C (mid-homophily pitfall), and larger structural homophily consistently improves graph-aware models.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Tri-Hom (J_G^h) instead of class homophily to estimate model-performance alignment | MLP · 31 real-world datasets | Pearson correlation: 0.6078 -> 0.5471 | Hurt |
| Use Tri-Hom (J_G^h) instead of class homophily to estimate model-performance alignment | GCN · 31 real-world datasets | Pearson correlation: 0.6120 -> 0.6650 | Helped |
| Use Tri-Hom (J_G^h) instead of aggregation homophily to estimate model-performance alignment | GraphSage · 31 real-world datasets | Pearson correlation: 0.6040 -> 0.6223 | Helped |
| Use Tri-Hom (J_G^h) instead of class homophily to estimate model-performance alignment | GAT · 31 real-world datasets | Pearson correlation: 0.6169 -> 0.6731 | Helped |
| Increase structural homophily | Graph-aware models · CSBM-3H | node distinguishability ratio | Helped |
| Increase label homophily | Graph-aware models · CSBM-3H, hL below 1/C | node distinguishability ratio | Helped |
| Increase label homophily | Graph-aware models · CSBM-3H, hL at or above 1/C | node distinguishability ratio | Hurt |
| Increase feature homophily | Graph-aware models · CSBM-3H | node distinguishability ratio | Mixed |
Surprising findings
- Feature homophily based on class-controlled or Dirichlet-type feature similarity is dependent on label homophily, so the authors argue existing feature metrics are redundant with label homophily.
- Feature shuffling within classes can improve GNN accuracy, which the theory attributes to structural-aware features at class boundaries.
Limitations
- Theory assumes class-balanced nodes, uniform node degrees, and linear feature dependencies.
- Estimating feature homophily on real data requires an extra assumption that intra-class distances of unobserved features are small.
- Correlation analysis is limited to 31 datasets and four GNN/MLP models with a fixed hyperparameter search.
Experimental setup
Datasets: Roman-Empire Amazon-Ratings Minesweeper Tolokers Questions Squirrel Chameleon Actor Texas Cornell Wisconsin Cora
Benchmarks: 31 real-world node classification datasets synthetic CSBM-3H graphs
Metrics: Pearson correlation node classification accuracy average rank of metrics Kendall's Tau
Baselines: edge homophily node homophily class homophily adjusted homophily label informativeness neighborhood similarity aggregation homophily generalized edge homophily class-controlled feature homophily classifier-based homophily
Builds on: Contextual Stochastic Block Model CSBM-H edge homophily node homophily graph convolutional network
Closest papers by meaning
- Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness–Generalization Perspective (NeurIPS 2025 · similarity 0.91)
- On the Impact of Feature Heterophily on Link Prediction with Graph Neural Networks (NeurIPS 2024 · similarity 0.91)
- Understanding Heterophily for Graph Neural Networks (ICML 2024 · similarity 0.89)
- When Hypergraph Meets Heterophily: New Benchmark Datasets and Baseline (AAAI 2025 · similarity 0.89)
- Homomorphism Counts for Graph Neural Networks: All About That Basis (ICML 2024 · similarity 0.89)
- Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering (AAAI 2024 · similarity 0.89)
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