Inference and reconstruction of biological networks from heterogeneous data is currently an active research subject with several important applications in systems biology. The problem has been attacked from many different points of view with varying degrees of success. In particular predicting new edges with a reasonable false discovery rate is highly demanded for practical applications, but remains extremely challenging due to the sparsity of the networks of interest. While most previous approaches based on the partial knowledge of the network to be inferred build global models to predict new edges over the network, we introduce here a novel method which predicts whether there is an edge from a newly added vertex to each of the vertices of a known network using local models. This involves learning individually a certain subnetwork associated with each vertex of the known network, then using the discovered classification rule associated with only that vertex to predict the edge to the new vertex. Excellent experimental results are shown in the case of metabolic and protein-protein interaction network reconstruction from a variety of genomic data.