Most recommendation systems in social networks provide users with relevant new friend suggestions by processing their personal information or their current friends lists. However, providing such recommendations may leak users' private information. We present a new differentially private recommendation algorithm that preserves the privacy of both attribute values and friend links. The algorithm mainly proceeds by adding calibrated noise to an adequate matrix representation of the social network. To get a good trade-off between privacy and accuracy, the required amount of noise should be limited and therefore we need to mitigate the prohibitive sensitivity of the matrix representation. For that, we apply a graph projection technique to control the size of friends lists. The effectiveness of our approach is demonstrated by experiments on real-world datasets and comparison with existing methods.