In this paper, we focus on the problem of preserving the privacy of sensitive relationships in graph data. We refer to the problem of inferring sensitive relationships from anonymized graph data as link re-identification. We propose five different privacy preservation strategies, which vary in terms of the amount of data removed (and hence their utility) and the amount of privacy preserved. We assume the adversary has an accurate predictive model for links, and we show experimentally the success of different link re-identification strategies under varying structural characteristics of the data.