Fairness-aware Graph Neural Networks (GNNs) often face a challenging trade-off, where prioritizing fairness may require compromising utility. In this work, we re-examine fairness through the lens of spectral graph theory, aiming to reconcile fairness and utility within the framework of spectral graph learning. We explore the correlation between sensitive features and spectrum in GNNs, using theoretical analysis to delineate the similarity between original sensitive features and those after convolution under different spectrum. Our analysis reveals a reduction in the impact of similarity when the eigenvectors associated with the largest magnitude eigenvalue exhibit directional similarity. Based on these theoretical insights, we propose FUGNN, a novel spectral graph learning approach that harmonizes the conflict between fairness and utility. FUGNN ensures algorithmic fairness and utility by truncating the spectrum and optimizing eigenvector distribution during the encoding process. The fairness-aware eigenvector selection reduces the impact of convolution on sensitive features while concurrently minimizing the sacrifice of utility. FUGNN further optimizes the distribution of eigenvectors through a transformer architecture. By incorporating the optimized spectrum into the graph convolution network, FUGNN effectively learns node representations. Experiments on six real-world datasets demonstrate the superiority of FUGNN over baseline methods. The codes are available at https://github.com/yushuowiki/FUGNN.

翻译：公平感知图神经网络（GNNs）常面临一个具有挑战性的权衡：优先考虑公平性可能需要牺牲效用。本文从谱图理论的视角重新审视公平性问题，旨在谱图学习框架内协调公平性与效用。我们探究了GNN中敏感特征与频谱之间的关联，通过理论分析刻画了不同频谱下原始敏感特征与卷积后敏感特征之间的相似性。分析表明，当与最大幅值特征值对应的特征向量呈现方向相似性时，相似性的影响会减弱。基于这些理论见解，我们提出了FUGNN——一种新颖的谱图学习方法，能够协调公平性与效用之间的冲突。FUGNN通过在编码过程中截断频谱并优化特征向量分布，确保算法公平性与效用。公平感知的特征向量选择减少了卷积对敏感特征的影响，同时最大限度地降低了对效用的牺牲。FUGNN进一步通过transformer架构优化特征向量分布。通过将优化后的频谱融入图卷积网络，FUGNN能有效学习节点表示。在六个真实数据集上的实验表明，FUGNN优于基线方法。代码发布于https://github.com/yushuowiki/FUGNN。