The goal of privacy-preserving social graph release is to protect individual privacy while preserving data utility. Community structure, which is an important global pattern of nodes, is a crucial data utility as it is fundamental to many graph analysis tasks. Yet, most existing methods with differential privacy (DP) commonly fall into edge-DP to sacrifice security in exchange for utility. Moreover, they reconstruct graphs from the local feature-extraction of nodes, resulting in poor community preservation. Motivated by this, we develop PrivCom, a strict node-DP graph release algorithm to maximize the utility on the community structure while maintaining a higher level of privacy. In this algorithm, to reduce the huge sensitivity, we devise a Katz index based private graph feature extraction method, which can capture global graph structure features while greatly reducing the global sensitivity via a sensitivity regulation strategy. Yet, under the condition that the sensitivity is fixed, the feature captured by the Katz index, which is presented in matrix form, requires privacy budget splits. As a result, plenty of noise is injected, mitigating global structural utility. To bridge this gap, we design a private eigenvector estimation method, which yields noisy eigenvectors from extracted low-dimensional vectors. Then, a dynamic privacy budget allocation method with provable utility guarantees is developed to preserve the inherent relationship between eigenvalues and eigenvectors, so that the utility of the generated noise Katz matrix is well maintained. Finally, we reconstruct the synthetic graph via calculating its Laplacian with the noisy Katz matrix. Experimental results confirm our theoretical findings and the efficacy of PrivCom.

隐私保护社交图谱发布的目标是在保护数据效用的同时保护个人隐私。社区结构是一种重要的全局节点模式，是一种至关重要的数据实用程序，因为它是许多图分析任务的基础。然而，大多数现有的差分隐私（DP）方法通常属于边缘DP，以牺牲安全性来换取实用性。此外，他们从节点的局部特征提取中重建图，导致社区保存不佳。受此启发，我们开发了 PrivCom，一种严格的节点 DP 图发布算法，以最大限度地提高社区结构的效用，同时保持更高级别的隐私。在该算法中，为了降低巨大的敏感性，我们设计了一种基于Katz索引的私有图特征提取方法，该方法可以捕获全局图结构特征，同时通过敏感性调节策略大大降低全局敏感性。然而，在敏感度固定的情况下，以矩阵形式呈现的Katz指数捕获的特征需要隐私预算分割。结果，注入了大量噪音，削弱了全局结构效用。为了弥补这一差距，我们设计了一种私有特征向量估计方法，该方法从提取的低维向量中产生噪声特征向量。然后，开发了一种具有可证明效用保证的动态隐私预算分配方法，以保留特征值和特征向量之间的内在关系，从而很好地保持了生成的噪声Katz矩阵的效用。最后，我们通过用噪声 Katz 矩阵计算拉普拉斯算子来重建合成图。实验结果证实了我们的理论发现和 PrivCom 的功效。