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We give a simple, computationally efficient, and node-differentially-privatealgorithm for estimating the parameter of an Erdos-Renyi graph---that is,estimating p in a G(n,p)---with near-optimal accuracy. Our algorithm nearlymatches the information-theoretically optimal exponential-time algorithm forthe same problem due to Borgs et al. (FOCS 2018). More generally, we give anoptimal, computationally efficient, private algorithm for estimating theedge-density of any graph whose degree distribution is concentrated on a smallinterval.

Efficiently Estimating Erdos-Renyi Graphs with Node Differential Privacy