Differentially private GNNs (Graph Neural Networks) have been recently
studied to provide high accuracy in various tasks on graph data while strongly
protecting user privacy. In particular, a recent study proposes an algorithm to
protect each user's feature vector in an attributed graph with LDP (Local
Differential Privacy), a strong privacy notion without a trusted third party.
However, this algorithm does not protect edges (friendships) in a social graph
or protect user privacy in unattributed graphs. It remains open how to strongly
protect edges with LDP while keeping high accuracy in GNNs.
In this paper, we propose a novel LDP algorithm called the DPRR
(Degree-Preserving Randomized Response) to provide LDP for edges in GNNs. Our
DPRR preserves each user's degree hence a graph structure while providing edge
LDP. Technically, we use Warner's RR (Randomized Response) and strategic edge
sampling, where each user's sampling probability is automatically tuned to
preserve the degree information. We prove that the DPRR approximately preserves
the degree information under edge LDP. We focus on graph classification as a
task of GNNs and evaluate the DPRR using two social graph datasets. Our
experimental results show that the DPRR significantly outperforms Warner's RR
and provides accuracy close to a non-private algorithm with a reasonable
privacy budget, e.g., epsilon=1