Deep learning has been successful in various domains including image recognition, speech recognition and natural language processing. However, the research on its application in graph mining is still in an early stage. Here we present Model R, a neural network model created to provide a deep learning approach to the link weight prediction problem. This model uses a node embedding technique that extracts node embeddings (knowledge of nodes) from the known links’ weights (relations between nodes) and uses this knowledge to predict the unknown links’ weights. We demonstrate the power of Model R through experiments and compare it with the stochastic block model and its derivatives. Model R shows that deep learning can be successfully applied to link weight prediction and it outperforms stochastic block model and its derivatives by up to 73% in terms of prediction accuracy. We analyze the node embeddings to confirm that closeness in embedding space correlates with stronger relationships as measured by the link weight. We anticipate this new approach will provide effective solutions to more graph mining tasks.