We propose a novel trust framework to address the issue of “Can Alice trust Bob on a service?” in large online social networks (OSNs). Many models have been proposed for constructing and calculating trust. However, two common shortcomings make them less practical, especially in large OSNs: the information used to construct trust is (1) usually too complicated to get or maintain, that is, it is resource consuming; and (2) usually subjective and changeable, which makes it vulnerable to vicious nodes. With those problems in mind, we focus on generating small trusted graphs for large OSNs, which can be used to make previous trust evaluation algorithms more efficient and practical. We show how to preprocess a social network (PSN) by developing a simple and practical user-domain-based trusted acquaintance chain discovery algorithm through using the small-world network characteristics of online social networks and taking advantage of “weak ties”. Then, we present how to build a trust network (BTN) and generate a trusted graph (GTG) with the adjustable width breadth-first search algorithms. To validate the effectiveness of our work and to evaluate the quality of the generated trusted graph, we conduct many experiments with the real data set from Epinions.com. Our work is the first that focuses on generating small trusted graphs for large online social networks, and we explore the stable and objective information (such as domain) for inferring trust.