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A challenging problem in multimedia recommendation is to model a variety of relations, such as social, friend, listening, or tagging ones in a unified framework and to exploit all these sources of information. In this paper, music recommendation problem is expressed as a hypergraph ranking problem, introducing group sparsity constraints. By doing so, one can control how the different data groups (i.e., sets of hypergraph vertices) affect the recommendation process. Experiments on a dataset collected from Last.fm demonstrate that the accuracy is significantly increased by exploiting the group structure of the data. Preliminary results are also presented for Greek folk music recommendation.