Protein-protein interaction network inference is addressed as an output kernel learning task through semi-supervised Output Kernel Regression. Working in the framework of RKHS theory for vector-valued functions, we establish a new representer theorem devoted to semi-supervised least square regression. We then apply it to get a new model and show its relevance using numerical experiments on artificial networks and a protein-protein interaction network dataset using a very low percentage of labeled proteins in a transductive setting.