Preserving Friendly-Correlations in Uncertain Graphs Using Differential Privacy

It is a challenging problem to preserve the friendly-correlations between individuals when publishing social-network data. To alleviate this problem, uncertain graph has been presented recently. The main idea of uncertain graph is converting an original graph into an uncertain form, where the correlations between individuals is an associated probability. However, the existing methods of uncertain graph lack rigorous guarantees of privacy and rely on the assumption of adversary's knowledge. In this paper we first introduced a general model for constructing uncertain graphs. Then, we proposed an algorithm under the model which is based on differential privacy and made an analysis of algorithm's privacy. Our algorithm provides rigorous guarantees of privacy and against the background knowledge attack. Finally, the algorithm we proposed satisfied differential privacy and showed feasibility in the experiments. And then, we compare our algorithm with (k, ε)-obfuscation algorithm in terms of data utility, the importance of nodes for network in our algorithm is similar to (k, ε)-obfuscation algorithm.