We explore the edge-flipping mechanism, a type of input perturbation, to release the directed graph under edge-local differential privacy. By using the noisy bi-degree sequence from the output graph, we construct the moment equations to estimate the unknown parameters in the $p_0$ model, which is an exponential family distribution with the bi-degree sequence as the natural sufficient statistic. We show that the resulting private estimator is asymptotically consistent and normally distributed under some conditions. In addition, we compare the performance of input and output perturbation mechanisms for releasing bi-degree sequences in terms of parameter estimation accuracy and privacy protection. Numerical studies demonstrate our theoretical findings and compare the performance of the private estimates obtained by different types of perturbation methods. We apply the proposed method to analyze the UC Irvine message network.

翻译：本文探讨了边翻转机制——一种输入扰动方法——在边局部差分隐私下发布有向图。通过利用输出图中含噪声的双向度序列，我们构建矩方程以估计$p_0$模型中的未知参数；该模型是指数族分布，其双向度序列作为自然充分统计量。我们证明，在一定条件下，所得隐私估计量具有渐近一致性且服从正态分布。此外，我们从参数估计精度和隐私保护效果两个维度，比较了发布双向度序列时输入扰动与输出扰动机制的性能。数值研究验证了理论结论，并对比了不同类型扰动方法所得隐私估计量的表现。我们将所提方法应用于分析加州大学欧文分校消息网络。