This work addresses the problem of completing a partially observed matrix where the entries are either ones or zeroes. This is typically called one-bit matrix completion or binary matrix completion. In this problem, the association among the rows and among the columns can be modeled through graph Laplacians. Since the Laplacians cannot be computed from the incomplete matrix, they must be simultaneously estimated while completing the matrix. We model the problem as graph regularized binary matrix completion where the graphs need to be learnt from the data. We proposed an algorithm based on an alternating minimization scheme, taking advantage of an efficient proximity-based inner solver. The algorithm is applied to the problem of collaborative filtering. Experiments on benchmark datasets with state-of-the-art techniques in collaborative filtering show that the proposed method improves over the rest by a considerable margin.