PHDP: Preserving Persistent Homology in Differentially Private Graph Publications

Online social networks (OSNs) routinely share and analyze user data. This requires protection of sensitive user information. Researchers have proposed several techniques to anonymize the data of OSNs. Some differential-privacy techniques claim to preserve graph utility under certain graph metrics, as well as guarantee strict privacy. However, each graph utility metric reveals the whole graph in specific aspects.We employ persistent homology to give a comprehensive description of the graph utility in OSNs. This paper proposes a novel anonymization scheme, called PHDP, which preserves persistent homology and satisfies differential privacy. To strengthen privacy protection, we add exponential noise to the adjacency matrix of the network and find the number of adding/deleting edges. To maintain persistent homology, we collect edges along persistent structures and avoid perturbation on these edges. Our regeneration algorithms balance persistent homology with differential privacy, publishing an anonymized graph with a guarantee of both. Evaluation result show that the PHDP-anonymized graph achieves high graph utility, both in graph metrics and application metrics.