Emergence of scale-free networks from ideal free distributions

This letter presents a class of network optimization processes that account for the emergence of scale-free network structures. We introduce a mathematical framework that captures the connectivity and growth dynamics of a network with an arbitrary initial topology. We show how selection via differential node fitness affects the proportion of connections a node makes to other nodes, and how a heavy-tailed connectivity behavior manifests itself from consecutive achievements of ideal free distributions (IFDs). Finally, we present simulation results that show how this class of networks may emerge even when consecutive IFDs are not perfectly reached. Copyright (c) EPLA, 2008.