Social recommendation systems that make use of the user's social information have recently attracted considerable attention. These recommendation approaches partly solve cold-start and data sparsity problems and significantly improve the performance of recommendation systems. The essence of social recommendation methods is to utilize the user's explicit social connections to improve recommendation results. However, this information is not always available in real-world recommender systems. In this paper, a solution to this problem of explicit social information unavailability is proposed. The existing user-item rating matrix is used to compute implicit social information, and then an ISRec (implicit social recommendation algorithm) which integrates this implicit social information and the user-item rating matrix for social recommendation is introduced. Experimental results show that our method performs much better than state-of-the-art approaches; moreover, complexity analysis indicates that our approach can be applied to very large datasets because it scales linearly with respect to the number of observations in the matrices.