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Graph neural networks (GNNs) have emerged as a powerful tool for analyzing and learning from complex data structured as graphs, demonstrating remarkable effectiveness in various applications, such as social network analysis, recommendation systems, and drug discovery. However, despite their impressive performance, the fairness problem has increasingly gained attention as a crucial aspect to consider. Existing research in graph learning focuses on either group fairness or individual fairness. However, since each concept provides unique insights into fairness from distinct perspectives, integrating them into a fair graph neural network system is crucial. To the best of our knowledge, no study has yet to comprehensively tackle both individual and group fairness simultaneously. In this paper, we propose a new concept of individual fairness within groups and a novel framework named Fairness for Group and Individual (FairGI), which considers both group fairness and individual fairness within groups in the context of graph learning. FairGI employs the similarity matrix of individuals to achieve individual fairness within groups, while leveraging adversarial learning to address group fairness in terms of both Equal Opportunity and Statistical Parity. The experimental results demonstrate that our approach not only outperforms other state-of-the-art models in terms of group fairness and individual fairness within groups, but also exhibits excellent performance in population-level individual fairness, while maintaining comparable prediction accuracy.