This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, meta-data and social features. As we demonstrate, our hybrid recommendation system is very versatile and incorporates several well-known methods while outperforming them. Particularly, we show on real-world data that our model overcomes w.r.t. two evaluation metrics the recommendation of models solely based on low-rank information, graph-based information or a combination of both.