Web-based social networking is increasingly gaining popularity due to the rapid development of computer networking technologies. However, social networking applications still cannot obtain a wider acceptance by many users due to some unresolved issues, such as trust, security, and privacy. In social networks, trust is mainly studied whether a remote user behaves as expected by an interested user via other users, who are respectively named trustee, trustor, and recommenders. A trust graph consists of a trustor, a trustee, some recommenders, and the trust relationships between them. In this paper, we propose a novel FlowTrust approach to model a trust graph with network flows, and evaluate the maximum amount of trust that can flow through a trust graph using network flow theory. FlowTrust supports multi-dimensional trust. We use trust value and confidence level as two trust factors. We deduce four trust metrics from these two trust factors, which are maximum flow of trust value, maximum flow of confidence level, minimum cost of uncertainty with maximum flow of trust, and minimum cost of mistrust with maximum flow of confidence. We also propose three FlowTrust algorithms to normalize these four trust metrics. We compare our proposed FlowTrust approach with the existing RelTrust and CircuitTrust approaches. We show that all three approaches are comparable in terms of the inferred trust values. Therefore, FlowTrust is the best of the three since it also supports multi-dimensional trust.