Random Network Arithmetic Model Of Growth

The theory of random network was independently introduced by Erd(?)s and Rényi. This is an interesting definition in graph theory. Recently, plenty of research and exploration has been done in this field. Many achievements have been gained. Meanwhile, there are numbers of unsolved problems waiting for people to resolve.In the existing papers, the vetex in the growing networks increase one by one, as time grows. However, this is not fit to the real networks. For example, the company stuff scale may grow doubly in a period of time. So we have to alter the growing mode of the nodes of the networks. In this paper, the statistical structural properties of a special model of growing networks which may be relevant to social networks are introduced and analyzed. Firstly the results of the research of random growing network will be simplily summarized. Then a model of growing random network, whose nodes are added following arithmetical is established. And the degree distribution, the size of average component, size of the giant component and so on are gained. And the statistical character with a static random graph is compared. And finally, a special randomly growing network is introduced.