Weighted directed networks with a differentially private bi-degree sequence

Qiuping Wang, Xiao Zhang, Jing Luo, Yang Ouyang and Qian Wang

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 2, 285-300

Abstract: The p0 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 p0 model has been established. However, the p0 model only focuses on binary edges. In many realistic networks, edges could be weighted, taking a set of finite discrete values. In this article, we further show that the moment estimators of the parameters based on the differentially private bi-degree sequence in the weighted p0 model are consistent and asymptotically normal. Numerical studies demonstrate our theoretical findings.

Date: 2022
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DOI: 10.1080/03610926.2020.1747630

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