Evolving network models under a dynamic growth rule

TL;DR

This paper investigates evolving network models with dynamic growth rules involving node addition and deletion governed by a logistic equation, revealing diverse degree distributions and nonstationary behaviors similar to real-world networks.

Contribution

It introduces a model combining node addition and deletion based on logistic growth, demonstrating how these mechanisms produce various degree distributions and nonstationary network properties.

Findings

Networks exhibit fat-tailed degree distributions similar to real systems.

Degree distributions can shift from power-law to exponential or Gaussian.

The model explains diverse topologies observed in real-world networks.

Abstract

Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where $P_a$ and $P_d$ are determined by the Logistic population equation, topological properties of networks are studied. All the fat-tailed degree distributions observed in real systems are obtained, giving the evidence that the mechanism of addition and deletion can lead to the diversity of degree distribution of real systems. Moreover, it is found that the networks exhibit nonstationary degree distributions, changing from the power-law to the exponential one or from the exponential to the Gaussian one. These results can be expected to shed some light on the formation and evolution of real complex real-world networks.