Recommendation systems aim to provide personalized predictions by identifying items that are most appealing to individual users. Among various recommendation approaches, k-nearest-neighbor (kNN)-based collaborative filtering (CF) remains one of the most widely used in practice. However, the kNN scheme often results in running the algorithm on a highly dense graph, which degrades computational efficiency. In addition, enforcing a uniform neighborhood size is not well suited to capturing the true underlying structure of the data. In this paper, we leverage recent advances in graph signal processing (GSP) to learn a sparse yet high-quality graph, improving the efficiency of collaborative filtering without sacrificing recommendation accuracy. Experiments on benchmark datasets demonstrate that our method can successfully perform CF-based recommendation using an extremely sparse graph while maintaining competitive performance.