In recent years, social networks have made significant development and are spreading rapidly. A social network can be modeled as a graph. So that, the vertices of the graph represent the people in network and the edges represent the relationships between entities in the social network. This modeling be caused to the graph theory has been widely considered in the analysis of social networks. Social network analysis makes collect a lot of data sources, including individuals and their relationships in the network that this information is a valuable resource for researchers in various fields, including social psychology, sociology, statistics, geography, economics, market research and so on. In the other hand the publication of these data sources can be a threat to users' privacy on a social network. So before the release of data for social network research purposes, require that data be anonymous. Anonymization is a very important process in order to ensure to thise issue that the social network data publication cause not violate users' privacy. Anonymous methods are divided into two major groups of graph modification approaches and the network graph clustering methods. In this thesis to study the preserving the privacy on social networks by clustering based anonymization.