The Degree Distribution of Random Birth-and-Death Network with Network Size Decline

TL;DR

This paper develops a method to exactly determine the degree distribution of a random birth-and-death network with declining size, revealing Poisson tail characteristics through analytical and simulation approaches.

Contribution

It introduces a general analytical framework for degree distributions in declining RBDNs, including exact solutions and tail behavior analysis.

Findings

Degree distributions follow a Poisson tail property.

The method is verified through computer simulations.

Analytical solutions are provided for specific parameters.

Abstract

In this paper, we provide a general method to obtain the exact solutions of the degree distributions for 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>2, 0<p<1/2 , then the average degree of network with n nodes is introduced to calculate the degree distribution. Especially, taking m=3 as an 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.