In this paper, we estimate the distribution of hidden nodes weights in large random graphs from the observation of very few edges weights. In this very sparse setting, the first non-asymptotic risk bounds for maximum likelihood estimators (MLE) are established. The proof relies on the construction of a graphical model encoding conditional dependencies that is extremely efficient to study n-regular graphs obtained using a round-robin scheduling. This graphical model allows to prove geometric loss of memory properties and deduce the asymp-totic behavior of the likelihood function. Following a classical construction in learning theory, the asymptotic likelihood is used to define a measure of performance for the MLE. Risk bounds for the MLE are finally obtained by subgaussian deviation results derived from concentration inequalities for Markov chains applied to our graphical model.