Edge Weight Differential Privacy Based Spectral Query Algorithm

The macro nature of social networks has always been a hot topic of scientific research, which is of great help in studying the characteristics of human social behavior. The spectrum is closely related to the nature of the network and determines certain information, including community division, loop, diameter, degree and so on. To ensure the security of data, the differential privacy security framework is used to propose three algorithms for privacy protection of edge weights in spectrum query. Firstly, the basic concepts of edge weight neighbor graph and edge weight difference privacy are given. For the single singular value query, the L1 global sensitivity of the function is proved, and an algorithm satisfying ε-differential privacy is designed by using Laplace mechanism. It can guarantee the privacy of edge weights when we query someone singular value. However, it cannot provide reasonable privacy protection for multiple singular value queries. So the L2 global sensitivity of the query for multiple singular values is further proved, and the Gaussian mechanism is used to design an algorithm that satisfies (ε, δ)-differential privacy. Finally, to combine with multi-singular values query strategy and spectral decomposition, a novel graph data publishing algorithm which can guarantee edge weight (ε, δ)-differential privacy is proposed. To verify the availability of these methods, experimental tests have been carried out in both model networks and actual networks, which shows that the algorithm can better guarantee the availability of data.