Research on the Evolutionary Model of A Kind of Vertex-splitting Network

Abstract

A problem is presented about the evolutionary process of the vertex splitting complex network. The rule of the evolution is: every newly-added vertex is the copy of or is split from the existing vertex. The analytic equation set of this network evolutionary model and arithmetic of iteration are put forward. A series of simulation calculation prove that the complex network is Scale Free Network and the power-law increases along with the increment of the splitting similarity degree of λ(t) and even approaches to +∞. When the initial degree of each new vertex is constant, the evolutionary process of the network is similar to that of the BA model.