Rating prediction is a key task of e-commerce recommendation mechanisms. Recent studies in social recommendation enhance the performance of rating predictors by taking advantage of user relationships. However, these prediction approaches mostly rely on user personal information which is a privacy threat. In this paper, we present dTrust, a simple social recommendation approach that avoids using user personal information. It relies uniquely on the topology of an anonymized trust-user-item network that combines user trust relations with user rating scores. This topology is fed into a deep feed-forward neural network. Experiments on real-world data sets showed that dTrust outperforms state-of-the-art in terms of Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) scores for both warm-start and cold-start problems.