Efficiently Estimating Erdos-Renyi Graphs with Node Differential Privacy

We give a simple, computationally efficient, and node-differentially-private algorithm for estimating the parameter of an Erdős-Rényi graph--that is, estimating p in a G(n, p)--with near-optimal accuracy. Our algorithm nearly matches the information-theoretically optimal exponential-time algorithm for the same problem due to Borgs et al. (FOCS 2018). More generally, we give an optimal, computationally efficient, private algorithm for estimating the edge-density of any graph whose degree distribution is concentrated in a small interval.