# Certifiable Robustness to Graph Perturbations

arXiv: https://arxiv.org/abs/1910.14356 · HTML: https://mlsanity.com/paper/1910.14356/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2019.

## Built on by (most cited first, 30 of 62)

- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [Robustness of Graph Neural Networks at Scale](https://mlsanity.com/paper/2110.14038/) (2021)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Robust Counterfactual Explanations on Graph Neural Networks](https://mlsanity.com/paper/2107.04086/) (2021)
- [Dissecting the Diffusion Process in Linear Graph Convolutional Networks](https://mlsanity.com/paper/2102.10739/) (2021)
- [Transferability of Graph Neural Networks: an Extended Graphon Approach](https://mlsanity.com/paper/2109.10096/) (2021)
- [Model Stealing Attacks Against Inductive Graph Neural Networks](https://mlsanity.com/paper/2112.08331/) (2021)
- [Single Node Injection Attack against Graph Neural Networks](https://mlsanity.com/paper/2108.13049/) (2021)
- [Understanding Structural Vulnerability in Graph Convolutional Networks](https://mlsanity.com/paper/2108.06280/) (2021)
- [SE-GSL: A General and Effective Graph Structure Learning Framework through Structural Entropy Optimization](https://mlsanity.com/paper/2303.09778/) (2023)
- [Interpretable Stability Bounds for Spectral Graph Filters](https://mlsanity.com/paper/2102.09587/) (2021)
- [Adversarial Training for Graph Neural Networks: Pitfalls, Solutions, and New Directions](https://mlsanity.com/paper/2306.15427/) (2023)
- [Model Inversion Attacks against Graph Neural Networks](https://mlsanity.com/paper/2209.07807/) (2022)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications](https://mlsanity.com/paper/2106.07767/) (2021)
- [Scalable Verification of GNN-based Job Schedulers](https://mlsanity.com/paper/2203.03153/) (2022)
- [Decentralized Inference with Graph Neural Networks in Wireless Communication Systems](https://mlsanity.com/paper/2104.09027/) (2021)
- [Stability of Graph Convolutional Neural Networks to Stochastic Perturbations](https://mlsanity.com/paper/2106.10526/) (2021)
- [Collective Robustness Certificates: Exploiting Interdependence in Graph Neural Networks](https://mlsanity.com/paper/2302.02829/) (2023)
- [A Simple and Yet Fairly Effective Defense for Graph Neural Networks](https://mlsanity.com/paper/2402.13987/) (2024)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [Localized Randomized Smoothing for Collective Robustness Certification](https://mlsanity.com/paper/2210.16140/) (2022)
- [Randomized Message-Interception Smoothing: Gray-box Certificates for Graph Neural Networks](https://mlsanity.com/paper/2301.02039/) (2023)
- [Verifying message-passing neural networks via topology-based bounds tightening](https://mlsanity.com/paper/2402.13937/) (2024)
- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [Hierarchical Randomized Smoothing](https://mlsanity.com/paper/2310.16221/) (2023)
- [Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attacks](https://mlsanity.com/paper/2404.17947/) (2024)
- [GraphAttacker: A General Multi-Task GraphAttack Framework](https://mlsanity.com/paper/2101.06855/) (2021)
- [Robust Graph Neural Networks via Unbiased Aggregation](https://mlsanity.com/paper/2311.14934/) (2023)

## Abstract (arXiv)

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks on both the graph structure and the node attributes. We propose the first method for verifying certifiable (non-)robustness to graph perturbations for a general class of models that includes graph neural networks and label/feature propagation. By exploiting connections to PageRank and Markov decision processes our certificates can be efficiently (and under many threat models exactly) computed. Furthermore, we investigate robust training procedures that increase the number of certifiably robust nodes while maintaining or improving the clean predictive accuracy.