Barlow Graph Auto-Encoder for Unsupervised Network Embedding
Abstract
Network embedding has emerged as a promising research field for network analysis. Recently, an approach, named Barlow Twins, has been proposed for self-supervised learning in computer vision by applying the redundancy-reduction principle to the embedding vectors corresponding to two distorted versions of the image samples. Motivated by this, we propose Barlow Graph Auto-Encoder, a simple yet effective architecture for learning network embedding. It aims to maximize the similarity between the embedding vectors of immediate and larger neighborhoods of a node, while minimizing the redundancy between the components of these projections. In addition, we also present the variation counterpart named as Barlow Variational Graph Auto-Encoder. Our approach yields promising results for inductive link prediction and is also on par with state of the art for clustering and downstream node classification, as demonstrated by extensive comparisons with several well-known techniques on three benchmark citation datasets.
Benchmark Results
Tested on 4 datasets 2 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 | |
| 3 | GAT+T | 0.9660
±0.0007 | |
| 7 | SAGE | 0.9643
±0.0027 | |
| 172 | BGRL | 0.9337
±0.0021 best reported | best today: Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learning (AAAI 2022) |
| 191 | GCA | 0.9320
±0.0060 best reported | best at pub: Calibrating and Improving Graph Contrastive Learning (TMLR 2021) best today: Decoupling Weighing and Selecting for Integrating Multiple Graph Pre-training Tasks (ICLR 2024) |
| 203 | GRACE | 0.9215 | prev best: Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning (IJCAI 2021) best today: Learn Beneficial Noise as Graph Augmentation (ICML 2025) |
| 206 | MVGRL | 0.9310
±0.0040 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: Decoupling Weighing and Selecting for Integrating Multiple Graph Pre-training Tasks (ICLR 2024) |
| 213 | DGI | 0.9309
±0.0008 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 262 | ARGA | 0.9268 | This paper |
| 267 | G-BT | 0.9263 | This paper |
| 285 | ARVGA | 0.9249 | This paper |
| 317 | VGAE | 0.9224 | prev best: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) Improvement within reported uncertainty; not highlighted. |
| 329 | GIC | 0.9211 | This paper |
| 351 | BGAE + Att | 0.9189 | This paper |
| 352 | GAE | 0.9168 | prev best: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: Graph Masked Autoencoders with Transformers (2022) Improvement within reported uncertainty; not highlighted. |
| 390 | MLP | 0.9128
±0.0063 | |
| 401 | BGAE | 0.9110 | This paper |
| 408 | GMI | 0.9081
±0.0015 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: Energy-Balanced Hyperspherical Graph Representation Learning via Structural Binding and Entropic Dispersion (2025) Difference within reported uncertainty; not counted as underperformance. |
| 444 | DeepWalk | 0.9005 | prev best: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 451 | BVGAE + Att | 0.8998 | This paper |
| 467 | BVGAE | 0.8938 | This paper |
| 537 | Raw | 0.7853 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphTARIF | 0.9461
±0.0017 | |
| 2 | GCN | 0.9412
±0.0008 | |
| 3 | GAT | 0.9398
±0.0022 | |
| 8 | SAGE | 0.9351
±0.0006 | |
| 17 | BGAE + Att | 0.9244 | This paper |
| 23 | BGAE | 0.9224 | This paper |
| 79 | BGRL | 0.9034
±0.0019 best reported | best today: Adaptive Negative Scheduling for Graph Contrastive Learning (2026) |
| 110 | BVGAE + Att | 0.8991 | This paper |
| 139 | GRACE | 0.8953
±0.0035 best reported | best today: Adaptive Negative Scheduling for Graph Contrastive Learning (2026) |
| 150 | BVGAE | 0.8919 | This paper |
| 160 | GCA | 0.8894 | prev best: Calibrating and Improving Graph Contrastive Learning (TMLR 2021) |
| 179 | MVGRL | 0.8861
±0.0064 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 202 | G-BT | 0.8814 | This paper |
| 210 | DGI | 0.8798
±0.0081 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: Bootstrap Latents of Nodes and Neighbors for Graph Self-Supervised Learning (2024) |
| 246 | VGAE | 0.8644 | prev best: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: HC-GAE: The Hierarchical Cluster-based Graph Auto-Encoder for Graph Representation Learning (NeurIPS 2024) Improvement within reported uncertainty; not highlighted. |
| 264 | GAE | 0.8666
±0.0007 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: Graph Masked Autoencoders with Transformers (2022) |
| 278 | DeepWalk | 0.8628 | prev best: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) Improvement within reported uncertainty; not highlighted. |
| 288 | ARVGA | 0.8602
±0.0011 best reported | |
| 293 | ARGA | 0.8586
±0.0011 best reported | |
| 315 | GIC | 0.8489 | This paper |
| 320 | MLP | 0.8463 | |
| 342 | GMI | 0.8422
±0.0052 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: Localized Graph Contrastive Learning (2022) |
| 457 | Raw | 0.7381 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GrokFormer | 0.9831
±0.0018 | |
| 2 | PolyFormer | 0.9808
±0.0027 | |
| 3 | SGFormer | 0.9796
±0.0081 | |
| 9 | GCN | 0.9774
±0.0035 | |
| 58 | MLP | 0.9597
±0.0007 | |
| 63 | GCA | 0.9590
±0.0020 best reported | best today: Unifying Graph Contrastive Learning with Flexible Contextual Scopes (2022) Difference within reported uncertainty; not counted as underperformance. |
| 69 | BGRL | 0.9580
±0.0040 best reported | best today: Unifying Graph Contrastive Learning with Flexible Contextual Scopes (2022) Difference within reported uncertainty; not counted as underperformance. |
| 77 | GRACE | 0.9574
±0.0006 best reported | best today: Learn Beneficial Noise as Graph Augmentation (ICML 2025) |
| 95 | BGAE + Att | 0.9564 | This paper |
| 103 | BVGAE + Att | 0.9560 | This paper |
| 125 | MVGRL | 0.9544
±0.0027 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 141 | G-BT | 0.9525
±0.0013 best reported | best today: Bootstrap Latents of Nodes and Neighbors for Graph Self-Supervised Learning (2024) Difference within reported uncertainty; not counted as underperformance. |
| 146 | GAE | 0.9520
±0.0010 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) best today: Revisiting Graph Autoencoders as Implicit Contrastive Learners (KDD 2024) |
| 153 | BVGAE | 0.9513 | This paper |
| 158 | BGAE | 0.9501 | This paper |
| 163 | DeepWalk | 0.9490 | prev best: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 167 | DGI | 0.9489
±0.0009 best reported | best at pub: Graph Contrastive Learning with Adaptive Augmentation (WWW 2020) |
| 174 | VGAE | 0.9452 | This paper |
| 181 | ARGA | 0.9432
±0.0004 best reported | |
| 183 | ARVGA | 0.9430 | This paper |
| 212 | Raw | 0.9358 | This paper |
| 235 | GIC | 0.9310 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GCN | 0.9302
±0.0011 | |
| 2 | RSE + RGCN (70b) | 0.8852
±0.0019 | |
| 3 | LEMP+T | 0.8825 | |
| 9 | SAGE | 0.8771 | |
| 94 | GRACE | 0.8014 | This paper |
| 100 | BGRL | 0.8000
±0.0010 best reported | best at pub: Large-Scale Representation Learning on Graphs via Bootstrapping (ICLR 2021) best today: PyG-SSL: A Graph Self-Supervised Learning Toolkit (2024) Difference within reported uncertainty; not counted as underperformance. |
| 112 | BGAE + Att | 0.7953 | This paper |
| 140 | BGAE | 0.7893 | This paper |
| 151 | DGI | 0.7865
±0.0690 best reported | best at pub: Graph Barlow Twins: A self-supervised representation learning framework for graphs (2021) best today: Quantizing Text-attributed Graphs for Semantic-Structural Integration (KDD 2025) Difference within reported uncertainty; not counted as underperformance. |
| 162 | GCA | 0.7840
±0.0013 best reported | best at pub: Graph Barlow Twins: A self-supervised representation learning framework for graphs (2021) best today: Augmentation-Free Graph Contrastive Learning with Performance Guarantee (2022) Difference within reported uncertainty; not counted as underperformance. |
| 181 | GAE | 0.7787
±0.0053 best reported | best today: Negative-Free Self-Supervised Gaussian Embedding of Graphs (2024) |
| 180 | VGAE | 0.7787
±0.0053 best reported | best today: Negative-Free Self-Supervised Gaussian Embedding of Graphs (2024) |
| 183 | BVGAE + Att | 0.7782 | This paper |
| 190 | MVGRL | 0.7757
±0.0046 best reported | best at pub: Graph Barlow Twins: A self-supervised representation learning framework for graphs (2021) best today: Negative-Free Self-Supervised Gaussian Embedding of Graphs (2024) Difference within reported uncertainty; not counted as underperformance. |
| 192 | BVGAE | 0.7752 | This paper |
| 197 | GIC | 0.7728 | This paper |
| 198 | DeepWalk | 0.7721 | prev best: Graph Barlow Twins: A self-supervised representation learning framework for graphs (2021) Improvement within reported uncertainty; not highlighted. |
| 211 | G-BT | 0.7683
±0.0073 best reported | best at pub: Graph Barlow Twins: A self-supervised representation learning framework for graphs (2021) best today: Negative-Free Self-Supervised Gaussian Embedding of Graphs (2024) Difference within reported uncertainty; not counted as underperformance. |
| 234 | GMI | 0.7490
±0.0010 best reported | best today: Learning Graph Augmentations to Learn Graph Representations (2022) Difference within reported uncertainty; not counted as underperformance. |
| 237 | MLP | 0.7469
±0.0085 | |
| 253 | Raw | 0.7198 | This paper |
| 278 | ARVGA | 0.6737 | This paper |
| 287 | ARGA | 0.6688 | This paper |
