  Graph neural networks (GNNs) have gained significant attraction due to their
expansive real-world applications. To build trustworthy GNNs, two aspects -
fairness and privacy - have emerged as critical considerations. Previous
studies have separately examined the fairness and privacy aspects of GNNs,
revealing their trade-off with GNN performance. Yet, the interplay between
these two aspects remains unexplored. In this paper, we pioneer the exploration
of the interaction between the privacy risks of edge leakage and the individual
fairness of a GNN. Our theoretical analysis unravels that edge privacy risks
unfortunately escalate when the nodes' individual fairness improves. Such an
issue hinders the accomplishment of privacy and fairness of GNNs at the same
time. To balance fairness and privacy, we carefully introduce fairness-aware
loss reweighting based on influence function and privacy-aware graph structure
perturbation modules within a fine-tuning mechanism. Experimental results
underscore the effectiveness of our approach in achieving GNN fairness with
limited performance compromise and controlled privacy risks. This work
contributes to the comprehensively developing trustworthy GNNs by
simultaneously addressing both fairness and privacy aspects.
