Social Internet-of-Things (IoT) enhances collaboration between devices by endowing IoT systems with social attributes. However, calculating trust between devices based on complex and dynamic social attributes-similar to trust formation mechanisms in human society-poses a significant challenge. To address this issue, this paper presents a new hypergraph-enabled self-supervised contrastive learning (HSCL) method to accurately determine trust values between devices. To implement the proposed HSCL, hypergraphs are first used to discover and represent high-order relationships based on social attributes. Hypergraph augmentation is then applied to enhance the semantics of the generated social hypergraph, followed by the use of a parameter-sharing hypergraph neural network to nonlinearly fuse the high-order social relationships. Additionally, a self-supervised contrastive learning method is utilized to obtain meaningful device embeddings by conducting comparisons among devices, hyperedges, and device-to-hyperedge relationships. Finally, trust values between devices are calculated based on device embeddings that encapsulate high-order social relationships. Extensive experiments reveal that the proposed HSCL method outperforms baseline algorithms in effectively distinguishing between trusted and untrusted nodes and identifying the most trusted node.