Complex cooperative networks from evolutionary preferential attachment

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.Support from the Ministerio de Educacio´n y Ciencia through the Ramo´n y Cajal Program (Y.M.) and grants FIS 2006 12781 C02 01, FIS 2005 00337, MOSAICO and NAN2004 9087 C03 03. A.S. is also supported by the Comunidad de Madrid (Spain) under grant SIMUMAT CM.Publicad