Degree distribution of random birth-and-death network with network size decline

In this paper, we provide a general method to obtain the exact solutions of the degree distributions for random birth-and-death network (RBDN) with network size decline. First, by stochastic process rules, the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 < p < 1/2, then the average degree of network with n nodes is introduced to calculate the degree distributions. Specifically, taking m = 3 for example, we explain the detailed solving process, in which computer simulation is used to verify our degree distribution solutions. In addition, the tail characteristics of the degree distribution are discussed. Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN. (paper)