The primary structure of proteins, that is their sequence, represents one of the most abundant set of experimental data concerning biomolecules. The study of correlations in families of co-evolving proteins by means of an inverse Ising-model approach allows to obtain information on their native conformation. Following up on a recent development along this line, we optimize the algorithm to calculate effective energies between the residues, validating the approach both back-calculating interaction energies in a model system, and predicting the free energies associated to mutations in real systems. Making use of these effective energies, we study the networks of interactions which stabilizes the native conformation of some well-studied proteins, showing that it display different properties than the associated contact network. * Electronic address: guido.tiana@unimi.it 1 arXiv:1307.1583v1 [q-bio.BM]