In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes of a pre-existent network, we study network growth and formation by proposing an evolutionary preferential attachment model, its main feature being that the capacity of a node to attract new links depends on a dynamical variable governed in turn by the node interactions. As a specific example, we focus on the problem of the emergence of cooperation by analyzing the formation of a social network with interactions given by the Prisoner's Dilemma. The resulting networks show many features of real systems, such as scale-free degree distributions, cooperative behavior and hierarchical clustering. Interestingly, results such as the cooperators being located mostly on nodes of intermediate degree are very different from the observations of cooperative behavior on static networks. The evolutionary preferential attachment mechanism points to an evolutionary origin of scale-free networks and may help understand similar feedback problems in the dynamics of complex networks by appropriately choosing the game describing the interaction of nodes.

Recent studies on the evolutionary dynamics of the Prisoner's Dilemma game in scale-free networks have demonstrated that the heterogeneity of the network interconnections enhances the evolutionary success of cooperation. In this paper we address the issue of how the characterization of the asymptotic states of the evolutionary dynamics depends on the initial concentration of cooperators. We find that the measure and the connectedness properties of the set of nodes where cooperation reaches fixation is largely independent of initial conditions, in contrast with the behavior of both the set of nodes where defection is fixed, and the fluctuating nodes. We also check for the robustness of these results when varying the degree heterogeneity along a one-parametric family of networks interpolating between the class of Erdös-Renyi graphs and the Barabási-Albert networks.

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PACS 89.75.Fb -Structures and organization in complex systems PACS 87.23.Kg -Dynamics of evolution PACS 89.65.-s -Social and economic systems Abstract -Recent results have shown that heterogeneous populations are better suited to support cooperation than homogeneous settings when the Prisoner's Dilemma drives the evolutionary dynamics of the system. The same occurs when the network growth is coevolving together with the evolutionary dynamics, which also gives rise to highly cooperative scale-free networks. In the latter case, however, the organization of cooperation is radically different with respect to the case in which the underlying network is static. In this paper we study the structure of cooperation in static networks grown together with evolutionary dynamics and show that the general belief that hubs can only be occupied by cooperators does not hold. Moreover, these scale-free networks support high levels of cooperation despite having defector hubs. Our results have several important implications for the explanation of cooperative behavior in scale-free networks and highlight the importance that the formation of complex systems have on its function.Evolutionary dynamics [1] has attracted a lot of interest in the physics community lately, in particular in the context of evolutionary games on graphs [2,3]. This is a most relevant problem both from the physics viewpoint as well as from its applications. Indeed, evolutionary games describe a local optimization dynamics, which is largely different from the hamiltonian dynamics that is the traditional physics paradigm. On the other hand, these problems are related to important biological and socioeconomical issues, such as the emergence of cooperation [4].To date, a great deal of work has been done on evolutionary game dynamics on fixed networks (see, e.g., [2] and references therein). Beginning with the pioneering work by Nowak and May [5], much research has focused on whether the chances of establishing cooperative behavior (if not global, at least to a large extent) are improved by (a)