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Register a new userThe exploration of the Adjacent Possible explains the emergence and evolution of social networks
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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.
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By means of extensive computer simulations, the authors consider the entangled coevolution of actions and social structure in a new version of a spatial Prisoners Dilemma model that naturally gives way to a process of social differentiation. Diverse social roles emerge from the dynamics of the system: leaders are individuals getting a large payoff who are imitated by a considerable fraction of the population, conformists are unsatisfied cooperative agents that keep cooperating, and exploiters are defectors with a payoff larger than the average one obtained by cooperators. The dynamics generate a social network that can have the topology of a small world network. The network has a strong hierarchical structure in which the leaders play an essential role in sustaining a highly cooperative stable regime. But disruptions affecting leaders produce social crises described as dynamical cascades that propagate through the network.
We study the evolutionary Prisoners Dilemma on two social networks obtained from actual relational data. We find very different cooperation levels on each of them that can not be easily understood in terms of global statistical properties of both networks. We claim that the result can be understood at the mesoscopic scale, by studying the community structure of the networks. We explain the dependence of the cooperation level on the temptation parameter in terms of the internal structure of the communities and their interconnections. We then test our results on community-structured, specifically designed artificial networks, finding perfect agreement with the observations in the real networks. Our results support the conclusion that studies of evolutionary games on model networks and their interpretation in terms of global properties may not be sufficient to study specific, real social systems. In addition, the community perspective may be helpful to interpret the origin and behavior of existing networks as well as to design structures that show resilient cooperative behavior.
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Zipfs, Heaps and Taylors laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the scaling of fluctuations for systems as diverse as written texts and cities, ecological systems and stock markets. Many modeling schemes have been proposed in literature to explain those laws, but only recently a modeling framework has been introduced that accounts for the emergence of those laws without deducing the emergence of one of the laws from the others or without ad hoc assumptions. This modeling framework is based on the concept of adjacent possible space and its key feature of being dynamically restructured while its boundaries get explored, i.e., conditional to the occurrence of novel events. Here, we illustrate this approach and show how this simple modelling framework, instantiated through a modified Polyas urn model, is able reproduce Zipfs, Heaps and Taylors laws within a unique self-consistent scheme. In addition the same modelling scheme embraces other less common evolutionary laws (Hoppes model and Dirichlet processes) as particular cases.
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