# Graphon Neural Networks and the Transferability of Graph Neural Networks

arXiv: https://arxiv.org/abs/2006.03548 · HTML: https://mlsanity.com/paper/2006.03548/

## Key facts

- Cited by 118 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2020.

## Built on by (most cited first, 30 of 118)

- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [GFT: Graph Foundation Model with Transferable Tree Vocabulary](https://mlsanity.com/paper/2411.06070/) (2024)
- [Theory of Graph Neural Networks: Representation and Learning](https://mlsanity.com/paper/2204.07697/) (2022)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [Non-IID Transfer Learning on Graphs](https://mlsanity.com/paper/2212.08174/) (2022)
- [OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs](https://mlsanity.com/paper/2205.15117/) (2022)
- [Knowledge Distillation on Graphs: A Survey](https://mlsanity.com/paper/2302.00219/) (2023)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Trees](https://mlsanity.com/paper/2412.16441/) (2024)
- [Graph Neural Networks with Adaptive Readouts](https://mlsanity.com/paper/2211.04952/) (2022)
- [On the Universality of Graph Neural Networks on Large Random Graphs](https://mlsanity.com/paper/2105.13099/) (2021)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Relational Deep Learning: Challenges, Foundations and Next-Generation Architectures](https://mlsanity.com/paper/2506.16654/) (2025)
- [Learning by Transference: Training Graph Neural Networks on Growing Graphs](https://mlsanity.com/paper/2106.03693/) (2021)
- [Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2303.11323/) (2023)
- [coVariance Neural Networks](https://mlsanity.com/paper/2205.15856/) (2022)
- [Explainable Brain Age Prediction using coVariance Neural Networks](https://mlsanity.com/paper/2305.18370/) (2023)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [Limits, approximation and size transferability for GNNs on sparse graphs via graphops](https://mlsanity.com/paper/2306.04495/) (2023)
- [Node-oriented Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2212.03654/) (2022)
- [RouteNet-Fermi: Network Modeling with Graph Neural Networks](https://mlsanity.com/paper/2212.12070/) (2022)
- [Subgraph Pooling: Tackling Negative Transfer on Graphs](https://mlsanity.com/paper/2402.08907/) (2024)
- [Generalization Bounds for Message Passing Networks on Mixture of Graphons](https://mlsanity.com/paper/2404.03473/) (2024)
- [A Manifold Perspective on the Statistical Generalization of Graph Neural Networks](https://mlsanity.com/paper/2406.05225/) (2024)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Graph Neural Networks: Methods, Applications, and Opportunities](https://mlsanity.com/paper/2108.10733/) (2021)
- [Graph Neural Tangent Kernel: Convergence on Large Graphs](https://mlsanity.com/paper/2301.10808/) (2023)

## 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.