  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.
