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We design algorithms for fitting a high-dimensional statistical model to alarge, sparse network without revealing sensitive information of individualmembers. Given a sparse input graph $G$, our algorithms output anode-differentially-private nonparametric block model approximation. Bynode-differentially-private, we mean that our output hides the insertion orremoval of a vertex and all its adjacent edges. If $G$ is an instance of thenetwork obtained from a generative nonparametric model defined in terms of agraphon $W$, our model guarantees consistency, in the sense that as the numberof vertices tends to infinity, the output of our algorithm converges to $W$ inan appropriate version of the $L_2$ norm. In particular, this means we canestimate the sizes of all multi-way cuts in $G$.  Our results hold as long as $W$ is bounded, the average degree of $G$ growsat least like the log of the number of vertices, and the number of blocks goesto infinity at an appropriate rate. We give explicit error bounds in terms ofthe parameters of the model; in several settings, our bounds improve on ormatch known nonprivate results.

Private Graphon Estimation for Sparse Graphs