In this paper we model relational random variables on the edges of a network using Gaussian processes (GPs). We describe appropriate GP priors, i.e., covariance functions, for directed and undirected networks connecting homogeneous or heterogenous nodes. The framework suggests an intimate connection between link prediction and transfer learning, which were traditionally two separate topics. We develop an efficient learning algorithm that can handle a large number of observations. The experimental results on several real-world data sets verify superior learning capacity.