Evolving Network Modeling Driven by the Degree Increase and Decrease Mechanism

TL;DR

This paper introduces a new network evolution model incorporating both degree increase and decrease mechanisms, extending traditional growth models to better reflect real dynamic systems with fluctuating vertex degrees.

Contribution

It proposes a novel degree-based evolving network model that accounts for both growth and reduction, supported by theoretical analysis and validation with real network data.

Findings

The model produces degree distributions with a long tail.

Simulation results match theoretical predictions.

Applicable to real-world dynamic networks.

Abstract

Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured with a dynamic evolution including network reduction in addition to network growth. In this paper, we propose a novel mechanism for evolving networks from the perspective of vertex degree. We construct a queueing system to describe the increase and decrease of vertex degree, which drives the network evolution. In our mechanism, the degree increase rate is regarded as a function positively correlated to the degree of a vertex, ensuring the preferential attachment in a new way. Degree distributions are investigated under two expressions of the degree increase rate, one of which manifests a ``long tail'', and another one varies with different values of parameters. In simulations, we compare our theoretical distributions with simulation results and also apply them to real networks, which presents the validity and applicability of our model.