Consistent Community Detection in Multi-Layer Networks with Heterogeneous Differential Privacy

As network becomes increasingly prevalent, significant attention has been devoted to addressing privacy issues 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 investigate the utility of community detection in multi-layer networks under a personalized edge-flipping mechanism.This mechanism enables data publishers to protect edge information based on each node's privacy preferences.Within this framework, the community structure under the multi-layer degree-corrected stochastic block model remains invariant after appropriate debiasing, making consistent community detection in privatized multi-layer networks achievable.Theoretically, we establish the consistency of community detection in the privatized multi-layer network, demonstrating the fundamental privacy-utility tradeoff