mlsanityData to 7 Oct 2026

Topological Graph Neural Networks

arXiv 2102.07835 ↗First posted 15 Feb 2021cs.LG math.AT stat.MLcited by 86

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Abstract (arXiv)

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.

Key facts. Cited by 86 papers in the map (data through 7 Oct 2026). Builds on 31 of its 65 references that are in the map. First posted on arXiv 15 Feb 2021.

Builds on

31 of 65 references.

References · 31

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
  4. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  5. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  6. 2017Deep Setscited by 1,394
  7. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  8. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 718
  9. 2020Benchmarking Graph Neural Networkscited by 672
  10. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  11. 2019Provably Powerful Graph Networkscited by 385
  12. 2017Residual Gated Graph ConvNetscited by 341
19 more
  1. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  2. 2020Can Graph Neural Networks Count Substructures?cited by 235
  3. 2019On the equivalence between graph isomorphism testing and function approximation with GNNscited by 172
  4. 2019A Survey on Graph Kernelscited by 148
  5. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
  6. 2019Topological Autoencoderscited by 124
  7. 2017Deep Learning with Topological Signaturescited by 113
  8. 2019Graph Filtration Learningcited by 68
  9. 2018On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Propertiescited by 63
  10. 2020Graph Kernels: State-of-the-Art and Future Challengescited by 63
  11. 2019Learning metrics for persistence-based summaries and applications for graph classificationcited by 57
  12. 2016On Valid Optimal Assignment Kernels and Applications to Graph Classificationcited by 49
  13. 2019Graph Kernels: A Surveycited by 43
  14. 2020Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistencecited by 26
  15. 2017On the Combinatorial Power of the Weisfeiler-Lehman Algorithmcited by 18
  16. 2015Continuation of Point Clouds via Persistence Diagramscited by 13
  17. 2020PersGNN: Applying Topological Data Analysis and Geometric Deep Learning to Structure-Based Protein Function Predictioncited by 7
  18. 2015Stabilizing the unstable output of persistent homology computationscited by 3
  19. 2015A Geometric Perspective on Sparse Filtrationscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 7; 2023: 20; 2024: 23; 2025: 21; 2026: 13.

86 papers.

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  1. 2022Structure-Aware Transformer for Graph Representation Learningcited by 191
  2. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  3. 2023Rethinking the Expressive Power of GNNs via Graph Biconnectivitycited by 119
  4. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  5. 2022Ordered Subgraph Aggregation Networkscited by 57
  6. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 38
  7. 2024Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressivenesscited by 38
  8. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  9. 2023WL meet VCcited by 30
  10. 2023Is Distance Matrix Enough for Geometric Deep Learning?cited by 22
  11. 2023Going beyond persistent homology using persistent homologycited by 21
  12. 2023Embedding in Recommender Systems: A Surveycited by 19
38 more
  1. 2023Curvature Filtrations for Graph Generative Model Evaluationcited by 18
  2. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 18
  3. 2023Differentiable Euler Characteristic Transforms for Shape Classificationcited by 18
  4. 2023Simplicial Representation Learning with Neural k-Formscited by 18
  5. 2022Affinity-Aware Graph Networkscited by 17
  6. 2023Continual Graph Learning: A Surveycited by 17
  7. 2022SGAT: Simplicial Graph Attention Networkcited by 16
  8. 2024Understanding Virtual Nodes: Oversquashing and Node Heterogeneitycited by 14
  9. 2023GRIL: A 2-parameter Persistence Based Vectorization for Machine Learningcited by 13
  10. 2024Weisfeiler-Leman at the margin: When more expressivity matterscited by 13
  11. 2024Tensor-view Topological Graph Neural Networkcited by 12
  12. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  13. 2024Boosting Graph Pooling with Persistent Homologycited by 9
  14. 2023Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Cloudscited by 8
  15. 2023Cycle Invariant Positional Encoding for Graph Representation Learningcited by 8
  16. 2023Union Subgraph Neural Networkscited by 6
  17. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  18. 2025Enhancing Graph Representation Learning with Localized Topological Featurescited by 6
  19. 2024GEFL: Extended Filtration Learning for Graph Classificationcited by 5
  20. 2024D-GRIL: End-to-End Topological Learning with 2-parameter Persistencecited by 5
  21. 2025The Flood Complex: Large-Scale Persistent Homology on Millions of Pointscited by 5
  22. 2022A Topological characterisation of Weisfeiler-Leman equivalence classescited by 3
  23. 2024Foundations and Frontiers of Graph Learning Theorycited by 3
  24. 2024CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphscited by 3
  25. 2024Conditional Uncertainty Quantification for Tensorized Topological Neural Networkscited by 3
  26. 2024Tensor-Fused Multi-View Graph Contrastive Learningcited by 3
  27. 2022On the Convergence of Optimizing Persistent-Homology-Based Lossescited by 2
  28. 2022Reduction Algorithms for Persistence Diagrams of Networks: CoralTDA and PrunITcited by 2
  29. 2023GLiDR: Topologically Regularized Graph Generative Network for Sparse LiDAR Point Cloudscited by 2
  30. 2023Permutation-Invariant Graph Partitioning:How Graph Neural Networks Capture Structural Interactions?cited by 2
  31. 2024Enhancing Topological Dependencies in Spatio-Temporal Graphs with Cycle Message Passing Blockscited by 2
  32. 2024PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extractioncited by 2
  33. 2024Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphscited by 2
  34. 2024Topological Data Analysis Applications in Natural Language Processing: A Surveycited by 2
  35. 2024Multiset Transformer: Advancing Representation Learning in Persistence Diagramscited by 2
  36. 2025LEAP: Local ECT-Based Learnable Positional Encodings for Graphscited by 2
  37. 2025On topological descriptors for graph productscited by 2
  38. 2026The Logical Expressiveness of Topological Neural Networkscited by 2

50 most cited of 86 All 86 (JSON)