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Predicting new links in a network is a problem of interest in many application domains. Most of the prediction methods utilize information on the network's entities, such as nodes, to build a model of links. Network structures are usually not used except for networks with similarity or relatedness semantics. In this paper, we use network structures for link prediction with a more general network type with latent feature models. The problem with these models is the computational cost to train the models directly for large data. We propose a method to solve this problem using kernels and cast the link prediction problem into a binary classification problem. The key idea is not to infer latent features explicitly, but to represent these features implicitly in the kernels, making the method scalable to large networks. In contrast to the other methods for latent feature models, our method inherits all the advantages of the kernel framework: optimality, efficiency, and nonlinearity. On sparse graphs, we show that our proposed kernels are close enough to the ideal kernels defined directly on latent features. We apply our method to real data of protein-protein interaction and gene regulatory networks to show the merits of our method.