Consistent community detection in multi-layer networks with heterogeneous differential privacy

TL;DR

This paper introduces a personalized edge-flipping mechanism that ensures differential privacy in multi-layer networks while maintaining community detection accuracy, balancing privacy and utility.

Contribution

It proposes a novel personalized edge-flipping method that achieves differential privacy and consistent community detection in multi-layer networks, with theoretical guarantees.

Findings

The mechanism preserves community structure under the multi-layer degree-corrected stochastic block model.

It provides differential privacy with variable privacy levels for different nodes.

Numerical experiments validate the effectiveness on synthetic and real-world networks.

Abstract

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.