  This paper presents a personalized graph federated learning (PGFL) framework
in which distributedly connected servers and their respective edge devices
collaboratively learn device or cluster-specific models while maintaining the
privacy of every individual device. The proposed approach exploits similarities
among different models to provide a more relevant experience for each device,
even in situations with diverse data distributions and disproportionate
datasets. Furthermore, to ensure a secure and efficient approach to
collaborative personalized learning, we study a variant of the PGFL
implementation that utilizes differential privacy, specifically
zero-concentrated differential privacy, where a noise sequence perturbs model
exchanges. Our mathematical analysis shows that the proposed privacy-preserving
PGFL algorithm converges to the optimal cluster-specific solution for each
cluster in linear time. It also shows that exploiting similarities among
clusters leads to an alternative output whose distance to the original solution
is bounded, and that this bound can be adjusted by modifying the algorithm's
hyperparameters. Further, our analysis shows that the algorithm ensures local
differential privacy for all clients in terms of zero-concentrated differential
privacy. Finally, the performance of the proposed PGFL algorithm is examined by
performing numerical experiments in the context of regression and
classification using synthetic data and the MNIST dataset.
