The rapid popularization of the social network platform is causing growing concern among users of personal privacy disclosure in social networks, and due to the characters of social network which have the large number of users and with complicated relationships, the traditional privacy preserving method cannot be applied to the social network privacy protection which have a number of users and complicated. Graph modification technique is a series of privacy preserving methods proposed for the privacy preserving of social network data. Uncertain graph is a privacy preserving method, which converting a deterministic graph into a probability graph. In this study, the edge probability assignment algorithm is mainly focused on in the uncertain graph, and an algorithm for assigning the edge probability assignment is proposed based on differential privacy. The algorithm has a double privacy protection, which is suitable for social networks with high privacy requirements. Meanwhile, a different algorithm of uncertain graphs' edge probability assignment is presented based on the triadic closure, which achieves privacy preserve while maintains high data utility and suitable for simple social networks. The analysis and comparison show that the algorithm for assigning the edge probabilities of uncertain graph based on differential privacy can achieve a higher privacy preserving which was compared with obfuscation algorithm, and the algorithm of uncertain graphs' edge probability assignment based on triadic closure has higher data utility. Finally, in order to measure the distortion of the network structure, a data utility measure is proposed based on network structure entropy. The algorithm can measure the similarity between the uncertain graph and the original structure.