Recent advances in the Internet of Things (IoT) have led to the rise of a new paradigm: Social Internet of Things (SIoT). However, the new paradigm, as inspired by the idea that smart objects will soon have a certain degree of social consciousness, is still in its infant state for several reasons. Most of the related works are far from embracing the social aspects of smart objects and the dynamicity of inter-object social relations. Furthermore, there is yet to be a coherent structure for organising and managing IoT objects that elicit social-like features. To fully understand how and to what extent these objects mimic the behaviours of humans, we first model SIoT by scrutinising the distinct characteristics and structural facets of human-centric social networks. To elaborate, we describe the process of profiling the IoT objects that become social and classify various inter-object social relationships. Afterwards, a novel discovery mechanism, which utilises our hypergraph-based overlay network model, is proposed. To test the feasibility of the proposed approach, we have performed several experiments on our smart home automation demo box built with various sensors and actuators.