The integration of social networking concepts into Internet of Things systems is a burgeoning topic of research that promises to support novel and more powerful applications. In this paper we focus on the design and implementation of a highly scalable Trust and Reputation Model for the Internet of Things based on the social approach that the COSMOS project introduces, as part of its final results. We create our model by combining popular solutions proposed for Peer-to-Peer and mobile ad-hoc networks and adapting them on the Internet of Things concept. Each Thing can compute the Trust index of another Thing based on its own experiences, while it has the capability of determining its Reputation Index either by consulting its other “friends” (Followees) or referring to the Platform, a management system used in COSMOS. The model is tested through simulations of the proposed social system, demonstrating the ability of TRM-SIoT to achieve the Social Exclusion of malicious nodes and collectives from the network, with low computational overhead and high scalability. Furthermore, due to the adaptive nature of the system, Social Reintegration of these nodes is also possible.