# Networked Inequality: Preferential Attachment Bias in Graph Neural Network Link Prediction

arXiv: https://arxiv.org/abs/2309.17417 · HTML: https://mlsanity.com/paper/2309.17417/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 69 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [Towards a Unified Framework for Fair and Stable Graph Representation Learning](https://mlsanity.com/paper/2102.13186/) (2021)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [Graph Neural Networks for Link Prediction with Subgraph Sketching](https://mlsanity.com/paper/2209.15486/) (2022)
- [Towards Intersectionality in Machine Learning: Including More Identities, Handling Underrepresentation, and Performing Evaluation](https://mlsanity.com/paper/2205.04610/) (2022)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Characterizing Intersectional Group Fairness with Worst-Case Comparisons](https://mlsanity.com/paper/2101.01673/) (2021)
- [On Generalized Degree Fairness in Graph Neural Networks](https://mlsanity.com/paper/2302.03881/) (2023)
- [RawlsGCN: Towards Rawlsian Difference Principle on Graph Convolutional Network](https://mlsanity.com/paper/2202.13547/) (2022)
- [Factoring the Matrix of Domination: A Critical Review and Reimagination of Intersectionality in AI Fairness](https://mlsanity.com/paper/2303.17555/) (2023)
- [Toward Degree Bias in Embedding-Based Knowledge Graph Completion](https://mlsanity.com/paper/2302.05044/) (2023)
- [FairEGM: Fair Link Prediction and Recommendation via Emulated Graph Modification](https://mlsanity.com/paper/2201.11596/) (2022)
- [Gaps in Information Access in Social Networks](https://mlsanity.com/paper/1903.02047/) (2019)
- [Team Power Dynamics and Team Impact: New Perspectives on Scientific Collaboration using Career Age as a Proxy for Team Power](https://mlsanity.com/paper/2108.04108/) (2021)

## Built on by (most cited first, 8 of 8)

- [Theoretical and Empirical Insights into the Origins of Degree Bias in Graph Neural Networks](https://mlsanity.com/paper/2404.03139/) (2024)
- [Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction](https://mlsanity.com/paper/2602.11802/) (2026)
- [Identifying and Correcting Label Noise for Robust GNNs via Influence Contradiction](https://mlsanity.com/paper/2601.17469/) (2026)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [k-hop Fairness: Addressing Disparities in Graph Link Prediction Beyond First-Order Neighborhoods](https://mlsanity.com/paper/2603.03867/) (2026)
- [Boundary Embedding Shaping with Adaptive Contrastive Learning for Graph Structural Disentanglement](https://mlsanity.com/paper/2606.20283/) (2026)
- [A Survey on GNN-based Link Prediction: Techniques, Applications, and Challenges](https://mlsanity.com/paper/2607.16198/) (2026)
- [Fairness in Link Prediction Beyond Demographic Parity: A Reproducibility Study](https://mlsanity.com/paper/2608.09899/) (2026)

## Abstract (arXiv)

Graph neural network (GNN) link prediction is increasingly deployed in citation, collaboration, and online social networks to recommend academic literature, collaborators, and friends. While prior research has investigated the dyadic fairness of GNN link prediction, the within-group (e.g., queer women) fairness and "rich get richer" dynamics of link prediction remain underexplored. However, these aspects have significant consequences for degree and power imbalances in networks. In this paper, we shed light on how degree bias in networks affects Graph Convolutional Network (GCN) link prediction. In particular, we theoretically uncover that GCNs with a symmetric normalized graph filter have a within-group preferential attachment bias. We validate our theoretical analysis on real-world citation, collaboration, and online social networks. We further bridge GCN's preferential attachment bias with unfairness in link prediction and propose a new within-group fairness metric. This metric quantifies disparities in link prediction scores within social groups, towards combating the amplification of degree and power disparities. Finally, we propose a simple training-time strategy to alleviate within-group unfairness, and we show that it is effective on citation, social, and credit networks.