A social approach can be exploited for the Internet of Things (IoT) to manage a large number of connected objects. These objects operate as autonomous agents to request and provide information and services to users. Establishing trustworthy relationships among the objects greatly improves the effectiveness of node interaction in the social IoT and helps nodes overcome perceptions of uncertainty and risk. However, there are limitations in the existing trust models. In this paper, a comprehensive model of trust is proposed that is tailored to the social IoT. The model includes ingredients such as trustor, trustee, goal, trustworthiness evaluation, decision, action, result, and context. Building on this trust model, we clarify the concept of trust in the social IoT in five aspects such as (1) mutuality of trustor and trustee, (2) inferential transfer of trust, (3) transitivity of trust, (4) trustworthiness update, and (5) trustworthiness affected by dynamic environment. With network connectivities that are from real-world social networks, a series of simulations are conducted to evaluate the performance of the social IoT operated with the proposed trust model. An experimental IoT network is used to further validate the proposed trust model.