Social structure emerges from the interaction and information exchange between individuals in a population. The emergence of groups in animal and human social systems suggests that such social structures are the result of a cooperative and cohesive society. Using graph based models, where nodes represent individuals in a population and edges represent communication pathways, we simulate individual influence and the communication of ideas in a population. Simulations of Dunbarâ€™s hypothesis (that natural group size in apes and humans arises from the transition from grooming behaviour to language or gossip) indicate that transmission rate and neighbourhood size accompany critical transitions of the order proposed in Dunbarâ€™s work. We demonstrate that critical levels of connectivity are required to achieve consensus in models that simulate individual influence.