# Uncertainty in Graph Neural Networks: A Survey

arXiv: https://arxiv.org/abs/2403.07185 · HTML: https://mlsanity.com/paper/2403.07185/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 76 of its 103 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 30 of 76)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2001.06216/) (2020)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Bayesian Graph Neural Networks with Adaptive Connection Sampling](https://mlsanity.com/paper/2006.04064/) (2020)
- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs](https://mlsanity.com/paper/2206.10071/) (2022)

## Built on by (most cited first, 23 of 23)

- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Uncertainty-Aware Graph Structure Learning](https://mlsanity.com/paper/2502.12618/) (2025)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Can Molecular Foundation Models Know What They Don't Know? A Simple Remedy with Preference Optimization](https://mlsanity.com/paper/2509.25509/) (2025)
- [Belief-Calibrated Multi-Agent Consensus Seeking for Complex NLP Tasks](https://mlsanity.com/paper/2510.06307/) (2025)
- [Credal Graph Neural Networks](https://mlsanity.com/paper/2512.02722/) (2025)
- [Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?](https://mlsanity.com/paper/2605.22593/) (2026)
- [Conditional Shift-Robust Conformal Prediction for Graph Neural Network](https://mlsanity.com/paper/2405.11968/) (2024)
- [Node Classification With Integrated Reject Option](https://mlsanity.com/paper/2412.03190/) (2024)
- [REGE: A Method for Incorporating Uncertainty in Graph Embeddings](https://mlsanity.com/paper/2412.05735/) (2024)
- [CRC-SGAD: Conformal Risk Control for Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2504.02248/) (2025)
- [How Particle System Theory Enhances Hypergraph Message Passing](https://mlsanity.com/paper/2505.18505/) (2025)
- [GNN's Uncertainty Quantification using Self-Distillation](https://mlsanity.com/paper/2506.20046/) (2025)
- [Variational Graph Convolutional Neural Networks](https://mlsanity.com/paper/2507.01699/) (2025)
- [Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds](https://mlsanity.com/paper/2512.10407/) (2025)
- [Softmax is not Enough (for Adaptive Conformal Classification)](https://mlsanity.com/paper/2602.19498/) (2026)
- [NetworkNet: A Deep Neural Network Approach for Random Networks with Sparse Nodal Attributes and Complex Nodal Heterogeneity](https://mlsanity.com/paper/2604.11673/) (2026)
- [Quantile-Free Uncertainty Quantification in Graph Neural Networks](https://mlsanity.com/paper/2605.04847/) (2026)
- [GATTA: Graph Active Learning with Test-Time Augmentation](https://mlsanity.com/paper/2608.15084/) (2026)
- [Rethinking Epistemic Uncertainty in Node Classification through Information Growth](https://mlsanity.com/paper/2610.03418/) (2026)
- [Uncertainty Quantification Is Indispensable for Reliable Connectome-Based Graph Learning: A Narrative Review and Case Study](https://mlsanity.com/paper/2610.08353/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have been extensively used in various real-world applications. However, the predictive uncertainty of GNNs stemming from diverse sources such as inherent randomness in data and model training errors can lead to unstable and erroneous predictions. Therefore, identifying, quantifying, and utilizing uncertainty are essential to enhance the performance of the model for the downstream tasks as well as the reliability of the GNN predictions. This survey aims to provide a comprehensive overview of the GNNs from the perspective of uncertainty with an emphasis on its integration in graph learning. We compare and summarize existing graph uncertainty theory and methods, alongside the corresponding downstream tasks. Thereby, we bridge the gap between theory and practice, meanwhile connecting different GNN communities. Moreover, our work provides valuable insights into promising directions in this field.