The development of Web 2.0 and the rapid growth of available data have led to the development of systems, such as recommendation systems (RSs), that can handle the information overload. However, RS performance is severely limited by sparsity and cold-start problems. Thus, this paper aims to alleviate these problems. To realize this objective, a new model is proposed by integrating three sources of information: a user-item matrix, explicit and implicit relationships. The core strategy of this study is to use the multi-step resource allocation (MSRA) method to identify hidden relations in social information. First, explicit social information is used to compute the similarity between each pair of users. Second, for each nonfriend pair of users, the MSRA method is applied to determine the probability of their relation. If the probability exceeds a threshold, a new relationship will be established. Then, all sources are incorporated into the Singular Value Decomposition (SVD) method to compute the missing prediction values. Furthermore, the stochastic gradient descent technique is applied to optimize the training process. Additionally, two real datasets, namely, Last.Fm and Ciao, are utilized to evaluate the proposed method. In terms of accuracy, the experiment results demonstrate that the proposed method outperforms eight state-of-the-art approaches: Heats, PMF, SVD, SR, EISR-JC, EISR-CN, EISR-PA and EISR-RAI.