# Marginal Nodes Matter: Towards Structure Fairness in Graphs

arXiv: https://arxiv.org/abs/2310.14527 · HTML: https://mlsanity.com/paper/2310.14527/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 74 references that are in the map.
- First posted on arXiv 23 Oct 2023.

## Builds on (most cited first, 30 of 42)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [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)
- [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)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [Compositional Fairness Constraints for Graph Embeddings](https://mlsanity.com/paper/1905.10674/) (2019)
- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [EDITS: Modeling and Mitigating Data Bias for Graph Neural Networks](https://mlsanity.com/paper/2108.05233/) (2021)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Fairness in Graph Mining: A Survey](https://mlsanity.com/paper/2204.09888/) (2022)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [Improving Fairness in Graph Neural Networks via Mitigating Sensitive Attribute Leakage](https://mlsanity.com/paper/2206.03426/) (2022)
- [Learning Fair Node Representations with Graph Counterfactual Fairness](https://mlsanity.com/paper/2201.03662/) (2022)
- [Deep Representation Learning for Social Network Analysis](https://mlsanity.com/paper/1904.08547/) (2019)
- [FMP: Toward Fair Graph Message Passing against Topology Bias](https://mlsanity.com/paper/2202.04187/) (2022)

## Built on by (most cited first, 2 of 2)

- [Mitigating Degree Bias Adaptively with Hard-to-Learn Nodes in Graph Contrastive Learning](https://mlsanity.com/paper/2506.05214/) (2025)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)

## Abstract (arXiv)

In social network, a person located at the periphery region (marginal node) is likely to be treated unfairly when compared with the persons at the center. While existing fairness works on graphs mainly focus on protecting sensitive attributes (e.g., age and gender), the fairness incurred by the graph structure should also be given attention. On the other hand, the information aggregation mechanism of graph neural networks amplifies such structure unfairness, as marginal nodes are often far away from other nodes. In this paper, we focus on novel fairness incurred by the graph structure on graph neural networks, named structure fairness. Specifically, we first analyzed multiple graphs and observed that marginal nodes in graphs have a worse performance of downstream tasks than others in graph neural networks. Motivated by the observation, we propose Structural Fair Graph Neural Network (SFairGNN), which combines neighborhood expansion based structure debiasing with hop-aware attentive information aggregation to achieve structure fairness. Our experiments show SFairGNN can significantly improve structure fairness while maintaining overall performance in the downstream tasks.