From scale-free to Erdos-Rényi networks.

We analyze a model that interpolates between scale-free and Erdos-Rényi networks. The model introduced generates a one-parameter family of networks and allows one to analyze the role of structural heterogeneity. Analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks. Finally, an application of the proposed model to the study of the percolation transition is presented.