The Affection of Exponential Growth on Scale-Free Network

The combination of growth and preferential attachment is responsible for the power-law distribution of vertices' degree in random networks, however there are many kinds of growing ways of real networks. Based on preferential attachment and exponential growth, the paper presents the analytical results which the vertices' degree of scale-free network follows power-law distribution ( ) and parameter satisfies. At same time we find that the preferential attachment is taken place in a dynamic local world and the size of the dynamic local world is in direct proportion to the size of whole networks. The paper also gives the analytical results of no-preferential attachment and exponential growth on random networks. At last, computer simulated results of the model illustrate these analytical results.