Asymptotic in a class of network models with an increasing sub-Gamma degree sequence

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. For differential privacy under sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this article, we release the degree sequences of the binary networks under a general noisy mechanism, with the discrete Laplace mechanism as a special case. We establish the asymptotic result, including both consistency and asymptotically normality, of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real-data example are provided to illustrate the asymptotic results.