Federated learning is a semi-distributed algorithm, where a server communicates with multiple dispersed clients to learn a global model. The federated architecture is not robust and is sensitive to communication and computational overloads due to its one-master multi-client structure. It can also be subject to privacy attacks targeting personal information on the communication links. In this work, we introduce graph federated learning (GFL), which consists of multiple federated units connected by a graph. We then show how graph homomorphic perturbations can be used to ensure the algorithm is differentially private. We conduct both convergence and privacy theoretical analyses and illustrate performance by means of computer simulations.