Differentially Private Social Graph Publishing with Nearest Neighbor Structure Preservation

The goal of privacy-preserving social graph publishing is to protect individual privacy while preserving graph utility. Node nearest neighbor structure is a crucial social graph utility as it is the basis for many graph analysis tasks. Most existing methods with differential privacy focus on preserving degree distribution yet neglect the maintenance of connections between nodes' neighbors. Moreover, they require massive noise added to mask the change of a single edge, thereby rendering poor utility on the neighbor structure. As a result, it is tough to preserve high utility on the neighbor structure under differential privacy. To tackle these problems, we propose Priv-NNS, a private graph publishing algorithm to preserve the neighbor structure while guaranteeing individual privacy. This algorithm first decomposes a graph into subgraphs via extracting a nearest neighbor structure around each node. Then to yield node vectors satisfying differential privacy while preserving the neighbor structure, we design a private graph encoding approach with structure-awareness, which learns topological features of the subgraph by maximizing the co-occurrence probability among nodes. During this process, a novel objective perturbation approach with a random term, only requiring a scalar noise rather than a vector noise, is devised to balance the neighbor structure retained against the noise injected. Through formal privacy analysis, we prove that the yielded synthetic graph obeys ε-edge differential privacy. Experimental results demonstrate that Priv-NNS preserves high utility on the neighbor structure.