The goal of privacy-preserving graph publishing is to protect individual privacy in released graph data while preserving data utility. Degree distribution, serving as fundamental operations for many graph analysis tasks, is a crucial data utility. Yet, existing methods using differential privacy (DP) cannot well preserve degree distribution, since they distill a graph into a set of structural statistics (e.g. $dK$-series, etc.) that only captures local degree correlations, and require massive noise added to mask the change of a single edge. Recently Generative Adversarial Network for graphs (NetGAN) plays a key role in machine learning, due to its ability to capture the local and global degree distribution of the graph via biased random walks. Further, it allows us to move the burden of privacy-preserving to the learning procedure of its discriminator, rather than the extracted structure features. Inspired by this, we propose Priv-GAN, a private publishing model based on NetGAN. Instead of distilling and then publishing graphs, we publish the Priv-GAN model that is trained using the original data in a DP manner. With Priv-GAN, data holders are able to produce synthetic graph data with degree distribution preservation. Compared to alternative solutions, ours highlights that (i) a private Langevin with gradient estimate is designed as an optimizer for discriminator, which provides a theoretical gradient upper bound and achieves DP by adding noise to the gradients; and (ii) importantly, the error bound of the noisy Langevin method is theoretically analyzed, which demonstrates that with appropriate parameter settings, Priv-GAN is able to maintain high utility guarantees. Experimental results confirm our theoretical findings and the efficacy of Priv-GAN.

保留隐私的图形发布的目标是在保留数据实用程序的同时，保护发布的图形数据中的个人隐私。度分布是许多图形分析任务的基本操作，是至关重要的数据实用程序。但是，使用差分隐私（DP）的现有方法不能很好地保留度数分布，因为它们将图提炼成一组结构统计信息（例如，$dķ$-系列等），仅捕获局部次数相关性，并且需要添加大量噪声以掩盖单个边缘的变化。最近，图的生成对抗网络（NetGAN）在机器学习中起着关键作用，因为它能够通过有偏的随机游走来捕获图的局部和全局程度分布。此外，它使我们可以将保护隐私的负担转移到其鉴别器的学习过程，而不是提取的结构特征上。受此启发，我们提出了一种基于NetGAN的私有发布模型Priv-GAN。代替提取图表然后发布图表，我们发布Priv-GAN模型，该模型使用DP方式使用原始数据进行训练。借助Priv-GAN，数据持有人能够生成具有度数分布保留的合成图形数据。与替代解决方案相比，我们的研究重点是：（i）带有梯度估计的私有兰格文被设计为鉴别器的优化器，它提供了理论上的梯度上限，并通过向梯度中添加噪声来实现DP；（ii）重要的是，从理论上分析了嘈杂的Langevin方法的误差范围，这表明通过适当的参数设置，Priv-GAN能够保持较高的效用保证。实验结果证实了我们的理论发现和Priv-GAN的功效。这表明，通过适当的参数设置，Priv-GAN能够保持较高的效用保证。实验结果证实了我们的理论发现和Priv-GAN的功效。这表明，通过适当的参数设置，Priv-GAN能够保持较高的效用保证。实验结果证实了我们的理论发现和Priv-GAN的功效。