An insertion-deletion-compensation model with Poisson process for scale-free networks

A novel insertion-deletion-compensation model with Poisson process for the scale-free complex network is explored. In the proposed model, a batch of newly added nodes are inserted into the network with the rate at λ under Poisson process and each new node is connected to some old nodes. Meanwhile, old nodes are possibly deleted due to aging or being attacked at each evolving time step. Furthermore, with a given probability, some additional links are preferentially incident to the nodes with better activity in the latest evolving periods. By mean field approach, we shows that the stationary mean degree distribution is a power-law distribution, and the power-law exponent is flexible and ranges from 1 to 3. By the aid of moment estimation in probability theory, we distinguish the convergence of node degree. Our theoretical result shows that the degree distribution and the power-law exponent of complex networks are kept unchanged and independent to the evolving time when the input rate and connections of individuals are not considered.