On the Privacy and Utility of Anonymized Social Networks

Abstract

One is either on Facebook or not. Of course, this assessment is controversial and its rationale arguable. It is nevertheless not far, for many, from the reason behind joining social media and publishing and sharing details of their professional and private lives. Not only the personal details that may be revealed, but also the structure of the networks are sources of invaluable information for any organization wanting to understand and learn about social groups, their dynamics and members. These organizations may or may not be benevolent. It is important to devise, design and evaluate solutions that guarantee some privacy. One approach that reconciles 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. In this paper, the authors try to empirically quantify the inevitable trade-off between utility and privacy. They do so for two state-of-the-art graph anonymization algorithms that protect against most structural attacks, the k-automorphism algorithm and the k-degree anonymity algorithm. The authors measure several metrics for a series of real graphs from various social media before and after their anonymization under various settings.

Graph Anonymization Using Machine Learning

“…A panel of utility metrics used in graphs can be found in Song et al [16]. Here we define 3 measures inspired from the literature to be computed on the anonymized graphs.…”

Preservation of Structural Properties in Anonymized Social Networks

“…It is worth noting that while the structural properties' values are significantly altered for kanonymous clustered social networks with large values of k, in particular for Enron and ScaleFree datasets, if a researcher has the additional knowledge of the model that the social network follows, then the original value, or more specifically the range for it, can be estimated with a good probability. It is also worth comparing our results and conclusions with the authors of [35] and [31]. In [35], the same anonymization model was used and the centrality measures were computed on the anonymized graph directly.…”

“…The reason of obtaining "better" results than those in [35] is the use of de-anonymized graphs (see Step 2 of our experimental framework) instead of the anonymized graphs, for computing structural properties values. In [31], the anonymization model used was k-automorphism. Their conclusion was "This comprehensive set of experiments on graphs from real social networks demonstrates that utility metrics are significantly impacted by k-automorphism anonymization" [31].…”

“…In [31], the anonymization model used was k-automorphism. Their conclusion was "This comprehensive set of experiments on graphs from real social networks demonstrates that utility metrics are significantly impacted by k-automorphism anonymization" [31]. Our results show significantly better results due to the selected model.…”

“…In addition to analyzing new structural properties, our approach is novel since we do not compute the structural properties values directly on the anonymized graph as in [35] (which have a reduced number of super-nodes and super-edges, thus generating less conclusive results ); instead, we generate for each anonymized graph, a subset of possible graphs that match the anonymized graph structure, and we compute the structural properties' values as the average of the corresponding values obtained for each "de-anonymized" graph. A second related work considers most of the structural properties from this paper except the topological indices measures [31]. It is worth mentioning that in the above mentioned paper the authors focus on a graph modification approach, k-automorphism, and they do not address any clustering-based anonymization model.…”