Weighted directed networks with a differentially private bi-degree sequence

作者：Wang, Qiuping^*; Zhang, Xiao; Luo, Jing^*; Ouyang, Yang; Wang, Qian

来源：COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2022, 51(2): 285-300.

DOI：10.1080/03610926.2020.1747630

• Asymptotic normality
• bi-degree
• consistency
• differential privacy

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 article, 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.