Recent trends show that the popularity of Social Networks (SNs) has been increasing rapidly. From daily communication sites to online communities, an average person's daily life has become dependent on these online networks. Additionally, the number of people using at least one of the social networks have increased drastically over the years. It is estimated that by the end of the year 2020, one-third of the world's population will have social accounts. Hence, user privacy protection has gained wide acclaim in the research community. It has also become evident that protection should be provided to these networks from unwanted intruders. In this dissertation, we consider data privacy on online social networks at the network level and the user level. The network-level privacy helps us to prevent information leakage to third-party users like advertisers. To achieve such privacy, we propose various schemes that combine the privacy of all the elements of a social network: node, edge, and attribute privacy by clustering the users based on their attribute similarity. We combine the concepts of k-anonymity and l-diversity to achieve user privacy. To provide user-level privacy, we consider the scenario of mobile social networks as the user location privacy is the much-compromised problem. We provide a distributed solution where users in an area come together to achieve their desired privacy constraints. We also consider the mobility of the user and the network to provide much better results.