Weighted directed networks with a differentially private bi-degree sequence

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.

KEYWORDS:

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

Acknowledgments

We are grateful to the two anonymous referees for useful comments and suggestions.

Additional information

Funding

Wang’s research is partially supported by the National Natural Science Foundation of China (No. 11771171). Luo’s research is partially supported by National Natural Science Foundation of China (No. 11801576) and by the Fundamental Research Funds for the Central Universities (South-Central University for Nationalities (CZQ19010)) and by National Statistical Science Research Project of China (No. 2019LY59).