Information Dynamics in Evolving Networks Based on the Birth-Death Process: Random Drift and Natural Selection Perspective

TL;DR

This paper models evolving networks using a birth-death process with Poisson arrivals and preferential attachment, analyzing how information spreads under random drift and natural selection perspectives.

Contribution

It introduces a Markov-based model for dynamic networks incorporating birth-death processes and studies information dynamics from stochastic and fitness-driven viewpoints.

Findings

Mean connection number influences random drift

Natural selection process unaffected by connection means

Stationary network properties derived from the model

Abstract

Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving networks with the birth-death of individuals. A new individual arrives at the group by the Poisson process, while new links are established in the network through either uniform connection or preferential attachment. Moreover, an existing individual has a limited lifespan before leaving the network. We determine stationary topological properties of these networks, including their size and mean degree. To address the effect of the birth-death evolution, we further study the information dynamics in the proposed network model from the random drift and natural selection perspective, based on assumptions of total-stochastic and fitness-driven evolution, respectively. In simulations, we analyze the fixation probability of individual information and find that means of new connections affect the random drift process but do not affect the natural selection process.