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Graph neural network (GNN) link prediction is increasingly deployed incitation, collaboration, and online social networks to recommend academicliterature, collaborators, and friends. While prior research has investigatedthe dyadic fairness of GNN link prediction, the within-group fairness and``rich get richer'' dynamics of link prediction remain underexplored. However,these aspects have significant consequences for degree and power imbalances innetworks. In this paper, we shed light on how degree bias in networks affectsGraph Convolutional Network (GCN) link prediction. In particular, wetheoretically uncover that GCNs with a symmetric normalized graph filter have awithin-group preferential attachment bias. We validate our theoretical analysison real-world citation, collaboration, and online social networks. We furtherbridge GCN's preferential attachment bias with unfairness in link predictionand propose a new within-group fairness metric. This metric quantifiesdisparities in link prediction scores between social groups, towards combatingthe amplification of degree and power disparities. Finally, we propose a simpletraining-time strategy to alleviate within-group unfairness, and we show thatit is effective on citation, online social, and credit networks.

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