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arXiv · 2003.11373

Weighted directed networks with a differentially private bi-degree sequence

Qiuping Wang·Xiao Zhang·Jing Luo·Yang Ouyang·Qian Wang
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Abstract

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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Qiuping Wang, Xiao Zhang, Jing Luo, Yang Ouyang, Qian Wang. 2020-03-21. Weighted directed networks with a differentially private bi-degree sequence. https://arxiv.org/abs/2003.11373

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