The Social Internet of Things (SIoT), integration of the Internet of Things and Social Networks paradigms, has been introduced to build a network of smart nodes that are capable of establishing social links. In order to deal with misbehaving service provider nodes, service requestor nodes must evaluate their trustworthiness levels. In this paper, we propose a novel trust management mechanism in the SIoT to predict the most reliable service providers for each service requestor, which leads to reduce the risk of being exposed to malicious nodes. We model the SIoT with a flexible bipartite graph (containing two sets of nodes: service providers and service requestors), then build a social network among the service requestor nodes, using the Hellinger distance. Afterward, we develop a social trust model using nodes' centrality and similarity measures to extract trust behaviors among the social network nodes. Finally, a matrix factorization technique is designed to extract latent features of SIoT nodes, find trustworthy nodes, and mitigate the data sparsity and cold start problems. We analyze the effect of parameters in the proposed trust prediction mechanism on prediction accuracy. The results indicate that feedbacks from the neighboring nodes of a specific service requestor with high Hellinger similarity in our mechanism outperforms the best existing methods. We also show that utilizing the social trust model, which only considers a similarity measure, significantly improves the accuracy of the prediction mechanism. Furthermore, we evaluate the effectiveness of the proposed trust management system through a real-world SIoT use case. Our results demonstrate that the proposed mechanism is resilient to different types of network attacks, and it can accurately find the most proper and trustworthy service provider.