Estimating the structure of Ising networks is a notoriously difficult problem. In this article it is demonstrated that using a latent variable representation of the Ising network, a full-data-information approach to uncover the network structure can be employed. Thereby, only ignoring information encoded in the prior distribution (of the latent variables). The full-data-information approach avoids having to compute the partition function and is thus computationally feasible, even for networks with many nodes. The full-data-information approach is illustrated with the estimation of dense networks.