计算机工程2025，Vol.51Issue(6)：20-28,9.DOI:10.19678/j.issn.1000-3428.0070532
有噪声加权无标度小世界网络的一致性问题
Consensus Problem of Noisy Weighted Scale-free Small-world Networks
摘要
Abstract
This study investigates the consensus problem,a fundamental issue in distributed systems and network control.Consensus studies have traditionally focused on unweighted networks,overlooking the impact of edge weights in real-world networks.However,networks such as transportation systems,social networks,and power networks exhibit significant weighted properties,and unweighted models fail to fully capture their complex interactions.To address this issuse,this study examines a cluster of pseudo-fractal-weighted networks to determine how edge weights affect consensus.The Laplacian matrix is used to establish a relationship between the Kirchhoff indices and network consensus,providing an in-depth analysis of consensus behavior in weighted networks.Through the calculation of recursive relations for various indices across iterations,precise formulas for key quantities such as the multiplicative Kirchhoff index,additive Kirchhoff index,Kirchhoff index,and network coherence are derived.A numerical analysis shows that as the network size increases,consensus in weighted networks converges to a constant,indicating greater resistance to external noise.关键词
加权网络/电阻距离/基尔霍夫指标/一致性问题/伪分形网络Key words
weighted network/resistance distance/Kirchhoff index/consensus problem/pseudo-fractal network分类
计算机与自动化引用本文复制引用
董宇泽,章忠志..有噪声加权无标度小世界网络的一致性问题[J].计算机工程,2025,51(6):20-28,9.基金项目
国家自然科学基金(62372112,61872093). （62372112,61872093）
