# Efficiently Estimating Erdos-Renyi Graphs with Node Differential Privacy

## TL;DR

This paper presents a simple, efficient, and nearly optimal node-differentially-private algorithm for estimating the parameter p in Erdos-Renyi graphs, with broader applicability to graphs with concentrated degree distributions.

## Contribution

It introduces a computationally efficient, private estimation algorithm that nearly matches the best possible accuracy of exponential-time methods for Erdos-Renyi graphs.

## Key findings

- Achieves near-optimal accuracy in estimating p in G(n,p)
- Provides an efficient private algorithm for estimating edge-density
- Extends to graphs with concentrated degree distributions

## Abstract

We give a simple, computationally efficient, and node-differentially-private algorithm for estimating the parameter of an Erdos-Renyi 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 on a small interval.