Evolving Network Modeling Driven by the Degree Increase and Decrease Mechanism

2023-09-01

IEEE Transactions on Systems, Man, and Cybernetics: Systems

AI Summary

Traditional network evolution models focus exclusively on growth, failing to capture the coexistence of network expansion and contraction observed in real-world systems. Method: We propose the first bidirectional dynamic evolution framework that jointly models both degree increase and decrease. Our approach introduces a queueing system to characterize degree evolution, incorporates network shrinkage mechanisms directly into the evolutionary model for the first time, and designs a novel rate-of-degree-change–based preferential attachment mechanism. Contribution/Results: Theoretical analysis and Monte Carlo simulations demonstrate that the model accurately reproduces two canonical degree distributions—long-tailed and parameter-sensitive types. Empirical validation across multiple real-world networks confirms its high predictive accuracy for degree distributions and strong explanatory power for structural dynamics. This work breaks the unidirectional growth paradigm, establishing a unified evolutionary theory capable of explaining both growth-dominated and contraction-coexisting regimes, while revealing a new degree-change-rate–driven preferential attachment mechanism.

Technology Category

• Machine Learning: Evolutionary Learning
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Applications and emergent phenomena
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Ever since the Barabási–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 article, 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 PA 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.

Problem

• Modeling network evolution with both growth and reduction dynamics
• Developing degree-driven mechanism using queueing theory
• Analyzing degree distributions under different parameter settings

Innovation

• Dynamic network evolution with degree increase and decrease
• Queueing system modeling vertex degree changes
• Preferential attachment via degree-correlated increase rate