Research On The Evolutionary Model Of A Kind Of Vertex-splitting Network

The inability of contemporary science to describe systems composed of nonidentical elements that have diverse and nonlocal interactions currently limits advances in many disciplines, ranging from molecular biology to computer science. Scale-free network is the net that obeys power-law distribution. BA model is the first model of the scale-free network, which catches two necessary formative mechanism of the Scale-free Network —increscent and preferential attachment and shows the reason that the large scale complicated net self-organizes to state of scale-free network. The publication of BA's paper starts the climax of the research in scale-free network and BA model. In the recent years of the new century, the scientists put forward many formative models of scale-free network and do some deep research in the main property of B A model.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.