M Is A Random Variable Degree Distribution Of Ba Model

Based on the method and techniques of Markov chain, this paper provides a rigorous proof for the existence and scale-free property of the degree distribution of the BA model, where m is a random variable.And the exact formula of the distribution is given. This paper is organized as follows.In chapter 1,we introduce the research background, status quo and the basic framework of this paper briefly. Chapter 2 introduces the preliminary knowledge,including the evolving history of complex network from the rules map to the random graph theory, network measurement characteristics,two typical complex networks(small-world networks and scale-free network),and several solutions of the network degree distribution.In chapter 3,we study the stability of the BA model with a random variable m.We give a proof the existence of the degree distribution, and its exact solutions are obtained.In chapter four, a summary is presents.We discuss the insufficiency of this paper and extended space.