The exploration of the Adjacent Possible explains the emergence and evolution of social networks

Abstract: The interactions among human beings represent the backbone of our societies. How people interact, establish new connections, and allocate their activities among these links can reveal a lot of our social organization. Despite focused attention by very diverse scientific communities, we still lack a first-principles modeling framework able to account for the birth and evolution of social networks. Here, we tackle this problem by looking at social interactions as a way to explore a very peculiar space, namely the adjacent possible space, i.e., the set of individuals we can meet at any given point in time during our lifetime. We leverage on a recent mathematical formalization of the adjacent possible space to propose a first-principles theory of social exploration based on simple microscopic rules defining how people get in touch and interact. The new theory predicts both microscopic and macroscopic features of social networks. The most striking feature captured on the microscopic side is the probability for an individual, with already $k$ connections, to acquire a new acquaintance. On the macroscopic side, the model reproduces the main static and dynamic features of social networks: the broad distribution of degree and activities, the average clustering coefficient and the innovation rate at the global and local level. The theory is born out in three diverse real-world social networks: the network of mentions between Twitter users, the network of co-authorship of the American Physical Society and a mobile-phone-call network.