Weighted directed networks with a differentially private bi-degree sequence
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The p_0 model is an exponential random graph model for directed networks with the bi-degree sequence as the exclusively sufficient statistic. It captures the network feature of degree heterogeneity. The consistency and asymptotic normality of a differentially private estimator of the parameter in the private p_0 model has been established. However, the p_0 model only focuses on binary edges. In many realistic networks, edges could be weighted, taking a set of finite discrete values. In this paper, we further show that the moment estimators of the parameters based on the differentially private bi-degree sequence in the weighted p_0 model are consistent and asymptotically normal. Numerical studies demonstrate our theoretical findings.
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