With the advent of the online social network and advancement of technology, people get connected and interact on social network. To better understand the behavior of users on social network, we need to mine the interactions of users and their demographic data. Companies with less or no expertise in mining would need to share this data with the companies of expertise for mining purposes. The major challenge in sharing the social network data is maintaining the individual privacy on social network while retaining the implicit knowledge embedded in the social network. Thus, there is a need of anonymizing the social network data before sharing it to the third-party. The current study proposes to use upper approximation concept of rough sets for developing a solution for privacy preserving social network graph publishing. The proposed algorithm is capable of preserving the privacy of graph structure while simultaneously maintaining the utility or value that can be generated from the graph structure. The proposed algorithm is validated by showing its effectiveness on several graph mining tasks like clustering, classification, and PageRank computation. The set of experiments were conducted on four standard datasets, and the results of the study suggest that the proposed algorithm would maintain the both the privacy of individuals and the accuracy of the graph mining tasks.