NCGNN: Node-Level Capsule Graph Neural Network for Semisupervised Classification
Abstract
Message passing has evolved as an effective tool for designing Graph Neural Networks (GNNs). However, most existing methods for message passing simply sum or average all the neighboring features to update node representations. They are restricted by two problems, i.e., (i) lack of interpretability to identify node features significant to the prediction of GNNs, and (ii) feature over-mixing that leads to the over-smoothing issue in capturing long-range dependencies and inability to handle graphs under heterophily or low homophily. In this paper, we propose a Node-level Capsule Graph Neural Network (NCGNN) to address these problems with an improved message passing scheme. Specifically, NCGNN represents nodes as groups of node-level capsules, in which each capsule extracts distinctive features of its corresponding node. For each node-level capsule, a novel dynamic routing procedure is developed to adaptively select appropriate capsules for aggregation from a subgraph identified by the designed graph filter. NCGNN aggregates only the advantageous capsules and restrains irrelevant messages to avoid over-mixing features of interacting nodes. Therefore, it can relieve the over-smoothing issue and learn effective node representations over graphs with homophily or heterophily. Furthermore, our proposed message passing scheme is inherently interpretable and exempt from complex post-hoc explanations, as the graph filter and the dynamic routing procedure identify a subset of node features that are most significant to the model prediction from the extracted subgraph. Extensive experiments on synthetic as well as real-world graphs demonstrate that NCGNN can well address the over-smoothing issue and produce better node representations for semisupervised node classification. It outperforms the state of the arts under both homophily and heterophily.
Benchmark Results
Tested on 5 datasets 8 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9703
±0.0019 | |
| 2 | GAT | 0.9669
±0.0014 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 3 | GAT+T | 0.9660
±0.0007 | |
| 7 | SAGE | 0.9643
±0.0027 | |
| 8 | GCN | 0.9632
±0.0008 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 21 | APPNP | 0.9196 | prev best: Spectral Graph Attention Network with Fast Eigen-approximation (2020) |
| 50 | SGC | 0.9049 | prev best: Spectral Graph Attention Network with Fast Eigen-approximation (2020) |
| 87 | GCNII | 0.9430
±0.0020 best reported | best today: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) |
| 214 | NCGNN-A | 0.9308 | This paper |
| 215 | Scattering GCN | 0.9307
±0.0042 best reported | best today: A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition (ICML 2024) |
| 233 | NCGNN-D | 0.9286 | This paper |
| 260 | DAGNN | 0.9269 | This paper |
| 322 | AdaEdge | 0.9222 | This paper |
| 324 | DropEdge | 0.9221 | This paper |
| 349 | JK-Net | 0.9190
±0.0070 best reported | Difference within reported uncertainty; not counted as underperformance. |
| 390 | MLP | 0.9128
±0.0063 | |
| 424 | BBGDC | 0.9059 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9461
±0.0017 | |
| 2 | GCN | 0.9412
±0.0008 best reported | best at pub: Learning on Attribute-Missing Graphs (2020) |
| 3 | GAT | 0.9398
±0.0022 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 8 | SAGE | 0.9351
±0.0006 | |
| 52 | GCNII | 0.9104
±0.0041 best reported | best today: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) |
| 58 | APPNP | 0.9093
±0.0018 best reported | best at pub: A Unified View on Graph Neural Networks as Graph Signal Denoising (2020) |
| 82 | SGC | 0.8338 | prev best: Graph-Revised Convolutional Network (2019) best today: SignGT: Signed Attention-based Graph Transformer for Graph Representation Learning (2023) Improvement within reported uncertainty; not highlighted. |
| 168 | Scattering GCN | 0.8883
±0.0044 best reported | best today: A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition (ICML 2024) |
| 204 | NCGNN-A | 0.8812 | This paper |
| 206 | NCGNN-D | 0.8811 | This paper |
| 320 | MLP | 0.8463 | |
| 324 | DAGNN | 0.8450
±0.0120 best reported | best today: Revisiting the Necessity of Graph Learning and Common Graph Benchmarks (2024) Difference within reported uncertainty; not counted as underperformance. |
| 398 | DropEdge | 0.8230 | This paper |
| 399 | AdaEdge | 0.8218 | This paper |
| 404 | JK-Net | 0.8200
±0.0060 best reported |
Heterophilic Graphs
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9672
±0.0147 | |
| 2 | DoG | 0.9660
±0.0210 | |
| 3 | GPF-plus | 0.9583
±0.0419 | |
| 34 | MLP | 0.8189 | prev best: Non-Local Graph Neural Networks (2020) best today: Design your own universe: a physics-informed agnostic method for enhancing graph neural networks (2024) Improvement within reported uncertainty; not highlighted. |
| 53 | GraphSAGE | 0.9000
±0.0365 | |
| 70 | GCNII | 0.8918
±0.0443 best reported | best today: Piecewise Constant Spectral Graph Neural Network (TMLR 2025) |
| 150 | H2GCN-1 | 0.8486 | This paper |
| 163 | NCGNN-A | 0.8443 | This paper |
| 203 | H2GCN-2 | 0.8216 | This paper |
| 211 | GAT | 0.8162
±0.0645 best reported | best at pub: Heterophilic Graphs (ICLR 2020) best today: Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models (2025) |
| 257 | GCN | 0.7933
±0.0447 best reported | best at pub: Non-Local Graph Neural Networks (2020) best today: Graph Wave Networks (WWW 2025) |
| 348 | Geom-GCN-S | 0.7350 best reported | best at pub: Non-Local Graph Neural Networks (2020) |
| 386 | DAGNN | 0.7027
±0.0493 best reported | |
| 416 | Geom-GCN-P | 0.6757 | This paper |
| 548 | Geom-GCN-I | 0.5758 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9541
±0.0272 | |
| 2 | ACM-GCN | 0.9480
±0.0380 | |
| 3 | RF-GCN | 0.9429 | |
| 24 | MLP | 0.9136
±0.0070 best reported | best at pub: Non-Local Graph Neural Networks (2020) best today: Node-oriented Spectral Filtering for Graph Neural Networks (2022) |
| 35 | GCNII | 0.8918
±0.0396 best reported | best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 118 | NCGNN-A | 0.8379 | This paper |
| 138 | SAGE | 0.8269 | |
| 153 | H2GCN-1 | 0.8216 | This paper |
| 154 | H2GCN-2 | 0.8216 | This paper |
| 158 | GAT | 0.5892 | prev best: Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Networks (NeurIPS 2020) best today: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 170 | GCN | 0.5703 | prev best: Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Networks (NeurIPS 2020) best today: Bayesian Neighborhood Adaptation for Graph Neural Networks (TMLR 2025) |
| 226 | Geom-GCN-S | 0.7540 best reported | best at pub: Non-Local Graph Neural Networks (2020) |
| 250 | DAGNN | 0.7351
±0.0718 best reported | |
| 370 | Geom-GCN-P | 0.6081 | This paper |
| 419 | Geom-GCN-I | 0.5676 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DiGGR | 0.4535
±0.0353 | |
| 2 | TRIGON | 0.4402
±0.0028 | |
| 3 | DoG | 0.4320
±0.0120 | |
| 38 | GCNII | 0.4082
±0.0179 best reported | best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 42 | MLP | 0.3576 | prev best: Non-Local Graph Neural Networks (2020) best today: Heterophily-Aware Graph Attention Network (2023) Improvement within reported uncertainty; not highlighted. |
| 68 | GraphSAGE | 0.3899
±0.0085 | |
| 135 | GCN | 0.3690 best reported | best at pub: Non-Local Graph Neural Networks (2020) best today: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 140 | NCGNN | 0.3684 | This paper |
| 182 | GAT | 0.3605
±0.0035 best reported | best at pub: Non-Local Graph Neural Networks (2020) best today: Hierarchical Graph Transformer with Adaptive Node Sampling (NeurIPS 2022) |
| 190 | H2GCN-1 | 0.3594
±0.0130 best reported | best today: Steering Graph Neural Networks with Pinning Control (2023) Difference within reported uncertainty; not counted as underperformance. |
| 204 | H2GCN-2 | 0.3562 | This paper |
| 211 | DAGNN | 0.3551
±0.0110 best reported | |
| 248 | Geom-GCN-S | 0.3460 best reported | best at pub: Non-Local Graph Neural Networks (2020) |
| 306 | Geom-GCN-P | 0.3163 best reported | best at pub: Heterophilic Graphs (ICLR 2020) |
| 371 | Geom-GCN-I | 0.2909 best reported | best at pub: Heterophilic Graphs (ICLR 2020) |
