The Study Of The Evolving Of The Complex Network

In recent years the investigating to complex networks attracts more and more attention. based on the fact that the degree distribution of many real complex networks displays power law format. The exponents measured for real networks vary between 1 and 3. In addition , the degree distribution of real networks can have nonpower-law features such as exponential cutoff or saturation for small k. Baralási and Albert proposed the revolutionary BA model of scale-free networks in 1999. As growing and preferential attachment mechanisms are incorporated in the evolution of BA network model, and the degree distribution of this model follows the power law format. The degree distribution of network reflects the hints of topology of the whole network . using nonequilibrium statistic method, Wenchen He gives time evolution of the degree distribution of A network model . S.N.Dorogovtsev and J.F.F Mendes proposed a wide class of developing and decaying networks . Their scaling properties are similar to BA network model by Baralási and Albert in the particular case of growing networks.In this paper, we give the scale of the connectivities of the developing network and the decaying network; at the same time we give the master equation satisfied by degree distribution of the evolving network, and obtain its rigorous analytical solution. The obtained solution is composed of two terms.. At infinite time of the evolution of this model , the normalized degree distribution is similar to the result of BA network model. C is equal to different value, and the topology of network is different. For c>0,the obtained solution is that one term decays as exponential way, well the other reflects the size effect. At finite time, the deviation of degree distribution from exponential format is introduced by size effect. For c→-1/2 ,the network resembles WS one . The structure is very homogeneous. At high enough rates of link removal, large clusters are certainly absent, the appearing structures indeed have to demonstrate quite different properties than networks with c≥0. Our result show that the permanent removing of links leads to a more essential change of a network than the addition of them. the decaying networks shows the evolution of network enough.