# Uncovering the Structural Fairness in Graph Contrastive Learning

arXiv: https://arxiv.org/abs/2210.03011 · HTML: https://mlsanity.com/paper/2210.03011/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 6 Oct 2022.

## Builds on (most cited first, 30 of 31)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [From Canonical Correlation Analysis to Self-supervised Graph Neural Networks](https://mlsanity.com/paper/2106.12484/) (2021)
- [Self-supervised Learning on Graphs: Contrastive, Generative,or Predictive](https://mlsanity.com/paper/2105.07342/) (2021)
- [Towards the Generalization of Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2111.00743/) (2021)
- [DEMO-Net: Degree-specific Graph Neural Networks for Node and Graph Classification](https://mlsanity.com/paper/1906.02319/) (2019)

## Built on by (most cited first, 29 of 29)

- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approach](https://mlsanity.com/paper/2506.13083/) (2025)
- [Graph Fairness Learning under Distribution Shifts](https://mlsanity.com/paper/2401.16784/) (2024)
- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Optimizing Long-tailed Link Prediction in Graph Neural Networks through Structure Representation Enhancement](https://mlsanity.com/paper/2407.20499/) (2024)
- [SAILOR: Structural Augmentation Based Tail Node Representation Learning](https://mlsanity.com/paper/2308.06801/) (2023)
- [Mitigating Degree Biases in Message Passing Mechanism by Utilizing Community Structures](https://mlsanity.com/paper/2312.16788/) (2023)
- [Toward Structure Fairness in Dynamic Graph Embedding: A Trend-aware Dual Debiasing Approach](https://mlsanity.com/paper/2406.13201/) (2024)
- [Node Duplication Improves Cold-start Link Prediction](https://mlsanity.com/paper/2402.09711/) (2024)
- [Theoretical and Empirical Insights into the Origins of Degree Bias in Graph Neural Networks](https://mlsanity.com/paper/2404.03139/) (2024)
- [GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks](https://mlsanity.com/paper/2410.09570/) (2024)
- [Towards Label Position Bias in Graph Neural Networks](https://mlsanity.com/paper/2305.15822/) (2023)
- [Equipping Federated Graph Neural Networks with Structure-aware Group Fairness](https://mlsanity.com/paper/2310.12350/) (2023)
- [Marginal Nodes Matter: Towards Structure Fairness in Graphs](https://mlsanity.com/paper/2310.14527/) (2023)
- [Fairness in Augmented Graph Learning: A Survey](https://mlsanity.com/paper/2504.21296/) (2025)
- [Benchmarking Bias Mitigation Toward Fairness Without Harm from Vision to LVLMs](https://mlsanity.com/paper/2602.03895/) (2026)
- [Migrate Demographic Group For Fair GNNs](https://mlsanity.com/paper/2306.04212/) (2023)
- [Understanding Community Bias Amplification in Graph Representation Learning](https://mlsanity.com/paper/2312.04883/) (2023)
- [CYCLE: Cross-Year Contrastive Learning in Entity-Linking](https://mlsanity.com/paper/2410.09127/) (2024)
- [FairACE: Achieving Degree Fairness in Graph Neural Networks via Contrastive and Adversarial Group-Balanced Training](https://mlsanity.com/paper/2504.09210/) (2025)
- [Mitigating Degree Bias in Graph Representation Learning with Learnable Structural Augmentation and Structural Self-Attention](https://mlsanity.com/paper/2504.15075/) (2025)
- [Mitigating Degree Bias Adaptively with Hard-to-Learn Nodes in Graph Contrastive Learning](https://mlsanity.com/paper/2506.05214/) (2025)
- [Model-Driven Graph Contrastive Learning](https://mlsanity.com/paper/2506.06212/) (2025)
- [Enhancing Contrastive Link Prediction With Edge Balancing Augmentation](https://mlsanity.com/paper/2508.14808/) (2025)
- [Understanding Fairness and Prediction Error through Subspace Decomposition and Influence Analysis](https://mlsanity.com/paper/2510.23935/) (2025)
- [Mitigating Bias in Graph Hyperdimensional Computing](https://mlsanity.com/paper/2512.07433/) (2025)
- [Exploring Topological Bias in Heterogeneous Graph Neural Networks](https://mlsanity.com/paper/2512.11846/) (2025)
- [Revisiting Positive Samples in Graph Contrastive Learning: From the Perspective of Message Passing](https://mlsanity.com/paper/2606.10284/) (2026)

## Abstract (arXiv)

Recent studies show that graph convolutional network (GCN) often performs worse for low-degree nodes, exhibiting the so-called structural unfairness for graphs with long-tailed degree distributions prevalent in the real world. Graph contrastive learning (GCL), which marries the power of GCN and contrastive learning, has emerged as a promising self-supervised approach for learning node representations. How does GCL behave in terms of structural fairness? Surprisingly, we find that representations obtained by GCL methods are already fairer to degree bias than those learned by GCN. We theoretically show that this fairness stems from intra-community concentration and inter-community scatter properties of GCL, resulting in a much clear community structure to drive low-degree nodes away from the community boundary. Based on our theoretical analysis, we further devise a novel graph augmentation method, called GRAph contrastive learning for DEgree bias (GRADE), which applies different strategies to low- and high-degree nodes. Extensive experiments on various benchmarks and evaluation protocols validate the effectiveness of the proposed method.