Differential Private Social Network Publication and Persistent Homology Preservation

Online social networks (OSNs) service providers share and analyze users’ data for better performance. Hence, they are responsible for the protection of sensitive information. Previous researchers proposed several anonymization techniques for OSN data. Some anonymization techniques based on differential privacy claim to preserve privacy and graph utility under certain graph metrics. However, these graph utility metrics can partially describe the whole graph. In this paper, we employ persistent homology to have a comprehensive description of the OSN graph utility. The proposed scheme novelly preserves the persistent structures and differential privacy. In the proposed scheme, we employ the adjacency matrix model as the graph abstraction model. To strengthen privacy protection, we add exponential noise to the adjacency matrix. We then find the number of adding/deleting edges under the guidance of differential privacy. To preserve persistent homology, we collect edges along with the persistent structures. The proposed scheme carefully perturbs the edges while preserving those structures. Two anonymization sub-schemes, PHDP and rPHDP, have been proposed to balance the computation complexity and utility preservation. The evaluation results show that the proposed scheme outperforms other traditional anonymization schemes under graph utility metrics and graph application metrics.