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Differentially private GNNs (Graph Neural Networks) have been recentlystudied to provide high accuracy in various tasks on graph data while stronglyprotecting user privacy. In particular, a recent study proposes an algorithm toprotect each user's feature vector in an attributed graph with LDP (LocalDifferential Privacy), a strong privacy notion without a trusted third party.However, this algorithm does not protect edges (friendships) in a social graph,hence cannot protect user privacy in unattributed graphs. How to provide strongprivacy with high accuracy in unattributed graphs remains open.  In this paper, we propose a novel LDP algorithm called the DPRR(Degree-Preserving Randomized Response) to provide LDP for edges in GNNs. OurDPRR preserves each user's degree hence a graph structure while providing edgeLDP. Technically, our DPRR uses Warner's RR (Randomized Response) and strategicedge sampling, where each user's sampling probability is automatically tunedusing the Laplacian mechanism to preserve the degree information under edgeLDP. We also propose a privacy budget allocation method to make the noise inboth Warner's RR and the Laplacian mechanism small. We focus on graphclassification as a task of GNNs and evaluate the DPRR using three social graphdatasets. Our experimental results show that the DPRR significantly outperformsthree baselines and provides accuracy close to a non-private algorithm in alldatasets with a reasonable privacy budget, e.g., epsilon=1.

Degree-Preserving Randomized Response for Graph Neural Networks under Local Differential Privacy