# On Calibration of Graph Neural Networks for Node Classification

arXiv: https://arxiv.org/abs/2206.01570 · HTML: https://mlsanity.com/paper/2206.01570/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 3 Jun 2022.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Towards Trustworthy Predictions from Deep Neural Networks with Fast Adversarial Calibration](https://mlsanity.com/paper/2012.10923/) (2020)
- [Meta-Cal: Well-controlled Post-hoc Calibration by Ranking](https://mlsanity.com/paper/2105.04290/) (2021)
- [On Focal Loss for Class-Posterior Probability Estimation: A Theoretical Perspective](https://mlsanity.com/paper/2011.09172/) (2020)
- [Are Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/1905.02296/) (2019)

## Built on by (most cited first, 9 of 9)

- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Unveiling Global Interactive Patterns across Graphs: Towards Interpretable Graph Neural Networks](https://mlsanity.com/paper/2407.01979/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Graph Isomorphic Networks for Assessing Reliability of the Medium-Voltage Grid](https://mlsanity.com/paper/2310.01181/) (2023)
- [BANGS: Game-Theoretic Node Selection for Graph Self-Training](https://mlsanity.com/paper/2410.09348/) (2024)
- [WATS: Calibrating Graph Neural Networks with Wavelet-Aware Temperature Scaling](https://mlsanity.com/paper/2506.23782/) (2025)
- [Towards Precise Prediction Uncertainty in GNNs: Refining GNNs with Topology-grouping Strategy](https://mlsanity.com/paper/2412.14223/) (2024)
- [Web Scale Graph Mining for Cyber Threat Intelligence](https://mlsanity.com/paper/2411.06239/) (2024)
- [HoTS: Homophily-Aware Temperature Scaling for Graph Neural Network Calibration](https://mlsanity.com/paper/2609.32426/) (2026)

## Abstract (arXiv)

Graphs can model real-world, complex systems by representing entities and their interactions in terms of nodes and edges. To better exploit the graph structure, graph neural networks have been developed, which learn entity and edge embeddings for tasks such as node classification and link prediction. These models achieve good performance with respect to accuracy, but the confidence scores associated with the predictions might not be calibrated. That means that the scores might not reflect the ground-truth probabilities of the predicted events, which would be especially important for safety-critical applications. Even though graph neural networks are used for a wide range of tasks, the calibration thereof has not been sufficiently explored yet. We investigate the calibration of graph neural networks for node classification, study the effect of existing post-processing calibration methods, and analyze the influence of model capacity, graph density, and a new loss function on calibration. Further, we propose a topology-aware calibration method that takes the neighboring nodes into account and yields improved calibration compared to baseline methods.