As network data has become increasingly prevalent, a substantial amount of attention has been paid to the privacy issue in publishing network data. One of the critical challenges for data publishers is to preserve the topological structures of the original network while protecting sensitive information. In this paper, we propose a personalized edge flipping mechanism that allows data publishers to protect edge information based on each node's privacy preference. It can achieve differential privacy while preserving the community structure under the multi-layer degree-corrected stochastic block model after appropriately debiasing, and thus consistent community detection in the privatized multi-layer networks is achievable. Theoretically, we establish the consistency of community detection in the privatized multi-layer network and show that better privacy protection of edges can be obtained for a proportion of nodes while allowing other nodes to give up their privacy. Furthermore, the advantage of the proposed personalized edge-flipping mechanism is also supported by its numerical performance on various synthetic networks and a real-life multi-layer network.

翻译：随着网络数据日益普遍，发布网络数据时的隐私问题受到了广泛关注。数据发布者面临的关键挑战之一是在保护敏感信息的同时，保持原始网络的拓扑结构。本文提出了一种个性化边翻转机制，允许数据发布者根据每个节点的隐私偏好来保护边信息。该机制在适当去偏后，能够在多层度校正随机块模型下实现差分隐私并保持社区结构，从而可在隐私化后的多层网络中进行一致的社区检测。理论上，我们证明了隐私化多层网络中社区检测的一致性，并表明在允许部分节点放弃隐私保护的情况下，可以为另一部分节点提供更好的边隐私保护。此外，所提出的个性化边翻转机制在各种合成网络和真实多层网络上的数值性能也验证了其优势。