The rising popularity of Web 2.0, such as blogs, forums, online calendars/diaries, etc., makes users more interested in keeping their data on the Web. Sharing of such data could make life more enjoyable and convenient. For example, posting new photos about activities or sharing views about an event can let friends know what a user cares about. However, some of these data (such as a person's location during a particular time, opinion about a political event, etc.) are private and should not be accessed by unauthorized users. Although Web 2.0 facilitates sharing, the fear of forwarding sensitive data to a third party without knowledge of the data owners discourages people from using certain applications due to privacy concerns. We take advantage of the existing relationships on social networks and build a "trust network" with transitive relationship to allow data sharing while respecting the privacy of data owners. The trust network linking private data owners, private data requesters, and intermediary users is a directed weighted graph. The permission value for each private data requester is automatically assigned in this network based on the transitive relationship. Experiments were conducted to confirm the feasibility of constructing the trust network from existing social networks, and to assess the appropriateness of permission value assignments in the query process. This privacy scheme can make private data sharing manageable by data owners, who only need to define the access rights of their closest contacts once.