Asymptotic in undirected random graph models with a noisy degree sequence

Abstract

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 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 model, -linear model, maximum entropy models with discrete weights.