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Graphon Neural Networks and the Transferability of Graph Neural Networks

arXiv 2006.03548 ↗First posted 5 Jun 2020cs.LG stat.MLcited by 117

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Abstract (arXiv)

Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envision using the same coefficients to define a GNN on another graph. This motivates analyzing the transferability of GNNs across graphs. In this paper we introduce graphon NNs as limit objects of GNNs and prove a bound on the difference between the output of a GNN and its limit graphon-NN. This bound vanishes with growing number of nodes if the graph convolutional filters are bandlimited in the graph spectral domain. This result establishes a tradeoff between discriminability and transferability of GNNs.

Key facts. Cited by 117 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jun 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2020: 1; 2021: 11; 2022: 27; 2023: 27; 2024: 21; 2025: 13; 2026: 17.

117 papers.

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  1. 2022G-Mixup: Graph Data Augmentation for Graph Classificationcited by 145
  2. 2022Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networkscited by 94
  3. 2024GFT: Graph Foundation Model with Transferable Tree Vocabularycited by 82
  4. 2022Theory of Graph Neural Networks: Representation and Learningcited by 60
  5. 2023Does Graph Distillation See Like Vision Dataset Counterpart?cited by 45
  6. 2022Non-IID Transfer Learning on Graphscited by 43
  7. 2021Transferability Properties of Graph Neural Networkscited by 42
  8. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  9. 2023Knowledge Distillation on Graphs: A Surveycited by 38
  10. 2023Taming Local Effects in Graph-based Spatiotemporal Forecastingcited by 37
  11. 2024Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Treescited by 30
  12. 2022Graph Neural Networks with Adaptive Readoutscited by 29
38 more
  1. 2021On the Universality of Graph Neural Networks on Large Random Graphscited by 26
  2. 2023Graph Deep Learning for Time Series Forecastingcited by 26
  3. 2021Learning by Transference: Training Graph Neural Networks on Growing Graphscited by 22
  4. 2025Relational Deep Learning: Challenges, Foundations and Next-Generation Architecturescited by 22
  5. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 21
  6. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  7. 2023Explainable Brain Age Prediction using coVariance Neural Networkscited by 19
  8. 2022coVariance Neural Networkscited by 18
  9. 2022Implicit Graphon Neural Representationcited by 18
  10. 2022Node-oriented Spectral Filtering for Graph Neural Networkscited by 17
  11. 2022RouteNet-Fermi: Network Modeling with Graph Neural Networkscited by 17
  12. 2023Limits, approximation and size transferability for GNNs on sparse graphs via graphopscited by 17
  13. 2024Subgraph Pooling: Tackling Negative Transfer on Graphscited by 17
  14. 2021Graph Neural Networks: Methods, Applications, and Opportunitiescited by 16
  15. 2023Graph Neural Tangent Kernel: Convergence on Large Graphscited by 16
  16. 2023Approximately Equivariant Graph Networkscited by 16
  17. 2024Generalization Bounds for Message Passing Networks on Mixture of Graphonscited by 16
  18. 2024A Manifold Perspective on the Statistical Generalization of Graph Neural Networkscited by 16
  19. 2024A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptationcited by 16
  20. 2021Wide and Deep Graph Neural Network with Distributed Online Learningcited by 14
  21. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 13
  22. 2023Fine-tuning Graph Neural Networks by Preserving Graph Generative Patternscited by 13
  23. 2025GRAVER: Generative Graph Vocabularies for Robust Graph Foundation Models Fine-tuningcited by 13
  24. 2020Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learningcited by 12
  25. 2021Training Stable Graph Neural Networks Through Constrained Learningcited by 12
  26. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 12
  27. 2023What functions can Graph Neural Networks compute on random graphs? The role of Positional Encodingcited by 11
  28. 2025Generative Graph Pattern Machinecited by 11
  29. 2021Robust Graph Neural Networks via Probabilistic Lipschitz Constraintscited by 10
  30. 2023Equivariant Neural Operator Learning with Graphon Convolutioncited by 10
  31. 2021Stability of Neural Networks on Manifolds to Relative Perturbationscited by 9
  32. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  33. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
  34. 2021Stability to Deformations of Manifold Filters and Manifold Neural Networkscited by 8
  35. 2022Convergence of Invariant Graph Networkscited by 8
  36. 2022Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphscited by 8
  37. 2023Zero-One Laws of Graph Neural Networkscited by 7
  38. 2023Stochastic Unrolled Federated Learningcited by 6

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