Social Internet of Things (SIoT) is a new standard resulting from the integration of the Internet of Things (IoT) and social networking. IoT is a visionary, one-paradigm, whereas social networks are platforms where voluminous collaborations between humans exist. The SIoT is defined as a social network of objects that are not only smarter but also socially conscious. Fundamental requirements of both IoT and SIoT networks include efficient service search and the discovery of object mechanisms. Therefore, our paper proposes a simple model for social networks to discover the object or services by using a small-world network. Our proposed model comprised a set of objects, and where each object is looking for a service. The service search is initiated in different hops by an object using a service query message to the nearest object. If the requested object is identified immediately or at the first hop, a permanent link is established between the service requester and the service provider otherwise the search process is repeated until the service is discovered. In this study, we integrate the SIoT with the small world concept for the building of our model. Our proposed model guarantees that the object containing the information is in a bounded path length and is treatable owing to the structure of small-world networks. The process of search is efficient because it is initiated only when an object asks for another object or service. Our intention here is to increase the navigability of the network. We carefully performed numerical analyses for our model and presented the simulation results based on efficiencies such as average path length, clustering coefficient, service execution time, and the giant component. After conducting various experiments, we conclude that our proposed model is efficient and reflects the real network structures of small-world networks, therefore, it can be suitable for social networks.