On the privacy and utility of anonymized social networks

You are on Facebook or you are out. Of course, this assessment is controversial and its rationale arguable. It is nevertheless not far, for many of us, from the reason behind our joining social media and publishing and sharing details of our professional and private lives. Not only the personal details we may reveal but also the very structure of the networks themselves are sources of invaluable information for any organization wanting to understand and learn about social groups, their dynamics and their members. These organizations may or may not be benevolent. It is therefore important to devise, design and evaluate solutions that guarantee some privacy. One approach that attempts to reconcile the different stakeholders' requirement is the publication of a modified graph. The perturbation is hoped to be sufficient to protect members' privacy while it maintains sufficient utility for analysts wanting to study the social media as a whole. It is necessarily a compromise. In this paper we try and empirically quantify the inevitable trade-off between utility and privacy. We do so for one state-of-the-art graph anonymization algorithm that protects against most structural attacks, the k-automorphism algorithm. We measure several metrics for a series of real graphs from various social media before and after their anonymization under various settings.