Random models of scale-free networks

In this paper, we study two models of network evolution and give more realistic descriptions of the local processes than Barabási-Albert model, incorporating the addition of new nodes, the addition of new links, the rewiring and deleting of links. To random networks model with single (or double) preferential attachment(s), we have proved that the two models are of scale-free networks if the parameters are chosen properly and got the scaling exponent γ by the continuum theory.