This paper presents a method for estimating the parameter of an Erdos-Renyi random graph model from a sample graph under node differential privacy. The paper contributes a novel algorithmic technique to achieve node DP via the smooth sensitivity framework which might be useful for other related problems. When preparing the final version of the paper the authors must address the presentation issues raised in the reviews, and in particular make the constants in the algorithms explicit to ensure the method can be implemented by practitioners.