Scale-free property of complex ad hoc networks with accelerated growth

Abstract

A complex ad hoc network model with accelerated growth is proposed in this paper. In the evolving process of the model, at each time step with the addition probability c 1 , a new vertex with m ( t ) edges is added into the model, which new adding edges are connected with the old vertices according to the preferential attachment rule. And with the deletion probability c 2 ( < c 1 ) , a random chosen vertex is deleted and its associated edges are disappeared simultaneously. The accelerated growth means that at each time step the number of new adding edges is the increasing function of the time t . We consider mainly m ( t ) = t θ , where 0 ⩽ θ ⩽ 1 , to analyze the degree distribution of the model. Using the continuous approach, we prove theoretically and numerically that the model follows the scale-free degree distribution and generates both the Barabási and Albert (BA) model and the model introduced by Sarshar and Roychowdhury (SR). In addition, we present the appropriate numerical range of c 1 , c 2 and θ according to theoretical analyzes and numerical simulation. The model takes on a certain universality to complex evolving network and has the guiding significance to the application of the peer-to-peer networks and complex ad hoc networks.