Title: Topology Matters in Fair Graph Learning: a Theoretical Pilot Study. Abstract: Recent advances in fair graph learning observe that graph neural networks (GNNs) further amplify prediction bias compared with multilayer perception (MLP), while the reason behind this is unknown. In this paper, we conduct a theoretical analysis of the bias amplification mechanism in GNNs. This is a challenging task since GNNs are difficult to be interpreted, and real-world networks are complex. To bridge the gap, we theoretically and experimentally demonstrate that aggregation operation in representative GNNs accumulates bias in node representation due to topology bias induced by graph topology. We provide a sufficient condition identifying the statistical information of graph data, so that graph aggregation enhances prediction bias in GNNs. 
 Motivated by this data-centric finding, we propose a fair graph refinement algorithm, named \textit{FairGR}, to rewire graph topology to reduce sensitive homophily coefficient while preserving useful graph topology. Experiments on node classification tasks demonstrate that \textit{FairGR} can mitigate the prediction bias with comparable performance on three real-world datasets. Additionally, \textit{FairGR} is compatible with many state-of-the-art methods, such as adding regularization, adversarial debiasing, and Fair mixup via refining graph topology. Therefore, \textit{FairGR} is a plug-in fairness method and can be adapted to improve existing fair graph learning strategies. 