# Training Robust Graph Neural Networks with Topology Adaptive Edge Dropping

arXiv: https://arxiv.org/abs/2106.02892 · HTML: https://mlsanity.com/paper/2106.02892/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 52 references that are in the map.
- First posted on arXiv 5 Jun 2021.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Learning to Drop: Robust Graph Neural Network via Topological Denoising](https://mlsanity.com/paper/2011.07057/) (2020)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Dual Graph Attention Networks for Deep Latent Representation of Multifaceted Social Effects in Recommender Systems](https://mlsanity.com/paper/1903.10433/) (2019)
- [Graph Neural Networks Exponentially Lose Expressive Power for Node Classification](https://mlsanity.com/paper/1905.10947/) (2019)
- [Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames](https://mlsanity.com/paper/1311.0897/) (2013)
- [Stability of Graph Neural Networks to Relative Perturbations](https://mlsanity.com/paper/1910.09655/) (2019)
- [Resource Allocation via Graph Neural Networks in Free Space Optical Fronthaul Networks](https://mlsanity.com/paper/2006.15005/) (2020)
- [Wide and Deep Graph Neural Networks with Distributed Online Learning](https://mlsanity.com/paper/2006.06376/) (2020)
- [Inter-cluster Transmission Control Using Graph Modal Barriers](https://mlsanity.com/paper/2010.04790/) (2020)

## Built on by (most cited first, 20 of 20)

- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [Graph Condensation: A Survey](https://mlsanity.com/paper/2401.11720/) (2024)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Learn Beneficial Noise as Graph Augmentation](https://mlsanity.com/paper/2505.19024/) (2025)
- [Wide and Deep Graph Neural Network with Distributed Online Learning](https://mlsanity.com/paper/2107.09203/) (2021)
- [GraphGLOW: Universal and Generalizable Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2306.11264/) (2023)
- [Graph Augmentation Learning](https://mlsanity.com/paper/2203.09020/) (2022)
- [RobGC: Towards Robust Graph Condensation](https://mlsanity.com/paper/2406.13200/) (2024)
- [Sparse Covariance Neural Networks](https://mlsanity.com/paper/2410.01669/) (2024)
- [Learning Stochastic Graph Neural Networks with Constrained Variance](https://mlsanity.com/paper/2201.12611/) (2022)
- [Learning Stable Graph Neural Networks via Spectral Regularization](https://mlsanity.com/paper/2211.06966/) (2022)
- [Causally-guided Regularization of Graph Attention Improves Generalizability](https://mlsanity.com/paper/2210.10946/) (2022)
- [On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks](https://mlsanity.com/paper/2312.02372/) (2023)
- [Revisiting Edge Perturbation for Graph Neural Network in Graph Data Augmentation and Attack](https://mlsanity.com/paper/2403.07943/) (2024)
- [Data Augmentation for Graph Data: Recent Advancements](https://mlsanity.com/paper/2208.11973/) (2022)
- [Graph Augmentation for Cross Graph Domain Generalization](https://mlsanity.com/paper/2502.18188/) (2025)
- [Edge Augmentation on Disconnected Graphs via Eigenvalue Elevation](https://mlsanity.com/paper/2207.05301/) (2022)
- [SpanGNN: Towards Memory-Efficient Graph Neural Networks via Spanning Subgraph Training](https://mlsanity.com/paper/2406.04938/) (2024)
- [Stochastic Sequential Decision Making over Expanding Networks with Graph Filtering](https://mlsanity.com/paper/2603.19501/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) are processing architectures that exploit graph structural information to model representations from network data. Despite their success, GNNs suffer from sub-optimal generalization performance given limited training data, referred to as over-fitting. This paper proposes Topology Adaptive Edge Dropping (TADropEdge) method as an adaptive data augmentation technique to improve generalization performance and learn robust GNN models. We start by explicitly analyzing how random edge dropping increases the data diversity during training, while indicating i.i.d. edge dropping does not account for graph structural information and could result in noisy augmented data degrading performance. To overcome this issue, we consider graph connectivity as the key property that captures graph topology. TADropEdge incorporates this factor into random edge dropping such that the edge-dropped subgraphs maintain similar topology as the underlying graph, yielding more satisfactory data augmentation. In particular, TADropEdge first leverages the graph spectrum to assign proper weights to graph edges, which represent their criticality for establishing the graph connectivity. It then normalizes the edge weights and drops graph edges adaptively based on their normalized weights. Besides improving generalization performance, TADropEdge reduces variance for efficient training and can be applied as a generic method modular to different GNN models. Intensive experiments on real-life and synthetic datasets corroborate theory and verify the effectiveness of the proposed method.