Asymptotic in undirected random graph models with a noisy degree sequence

In the case of differential privacy under the Laplace mechanism, the asymptotic properties of parameter estimator have been derived in some special models such as β− model, but under a general noisy mechanism, the results are lacking. In this article, we release the degree sequences of undirected weighted networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish a unified asymptotic result including the consistency and asymptotically normality of the parameter estimator. We apply it to the β− model, log -linear model, maximum entropy models with discrete weights.