Preserving Graph Utility in Anonymized Social Networks? A Study on the Persistent Homology

Abstract

Following the trend of privacy preserving online social network publishing, various anonymization mechanisms have been designed and employed. Many differential privacy-based mechanisms claim that they can preserve the utility as well as guarantee the privacy. Their utility analysis are always based on some specifically chosen metrics.This paper aims to find a novel angle that describing the network in multiple scales. Persistent homology is such a high level metric that it reveals the parameterized topological features with various scales and it is applicable for read-world applications. In this paper, four differential privacy mechanisms employing different models are analyzed under the traditional graph metrics and the persistent homology. The evaluation results demonstrate that all algorithms can partially or conditionally preserve certain traditional graph utilities, but none of them are suitable for all metrics. Furthermore, none of the existing mechanisms can fully preserve the persistent homology, especially in high dimensions, which implies that the true graph utility is lost.