Contact processes on scale-free networks

We investigate the contact process on random graphs generated from the configuration model for scale-free complex networks with the power law exponent . . (2, 3]. Using the neighborhood expansion method, we show that, with positive probability, any disease with an infection rate . > 0 can survive for exponential time in the number of vertices of the graph. This strongly supports the view that stochastic scale-free networks are remarkably different from traditional regular graphs, such as Z d and classical Erd.s-Rényi random graphs