Random Birth-and-Death Networks

Abstract

In this paper, a baseline model termed as random birth-and-death network model (RBDN) is considered, in which at each time step, a new node is added into the network with probability p (0<p <1) connect it with m old nodes uniformly, or an existing node is deleted from the network with probability q=1-p. This model allows for fluctuations in size, which may reach many different disciplines in physics, ecology and economics. The purpose of this study is to develop the RBDN model and explore its basic statistical properties. For different p, we first discuss the network size of RBDN. And then combining the stochastic process rules (SPR) based Markov chain method and the probability generating function method, we provide the exact solutions of the degree distributions. Finally, the characteristics of the tail of the degree distributions are explored after simulation verification. Our results show that the tail of the degree distribution for RBDN exhibits a Poisson tail in the case of 0<p<=1/2 and an exponential tail as p approaches to 1.

References in corpus (4)

• Temporal Networks
• Burstiness and aging in social temporal networks
• Addition-Deletion Networks
• Evolving networks through deletion and duplication

Cited by in corpus (6)

• Information Dynamics in Evolving Networks Based on the Birth-Death Process: Random Drift and Natural Selection Perspective
• Complex Network Modelling with Power-law Activating Patterns and Its Evolutionary Dynamics
• Temporal network modeling with online and hidden vertices based on the birth and death process
• Evolving Network Modeling Driven by the Degree Increase and Decrease Mechanism
• Stochastic resetting in a networked multiparticle system with correlated transitions
• A Class of Random Recursive Tree Algorithms with Deletion