Edge-Covariate Differential Privacy for Covariate-Assisted Networks

Differential privacy has become a crucial tool for protecting sensitive information. In network data, both the existence of edges and their associated covariates may reveal private details, making their unprotected release a serious privacy concern. However, most existing approaches to edge privacy fail to account for the protection of edge-specific covariates. In this paper, we address this gap by proposing a unified framework for safeguarding both edges and edge-wise covariates in covariate-assisted network models. We introduce edge-covariate differential privacy, a privacy notion designed to simultaneously protect the presence of edges and their associated covariates. To assess its impact on network modeling, we investigate the fundamental privacy–utility tradeoff of parameter estimation under a joint latent space model. Our approach employs a mixed privatization mechanism that combines randomized response for edges with a Laplace mechanism for covariates. We establish asymptotic consistency and minimax optimality, up to logarithmic factors, for parameter estimation under this privacy constraint. Extensive simulation studies and an application to a real-world citation network demonstrate that our method achieves a favorable balance between strong privacy guarantees and estimation accuracy.