具有合成网络结构的分层赋权图指标综述
A Review of Graph Indices of Composite Networks with Weighted and Layered Structures
DOI: 10.12677/aam.2025.1411475, PDF,    科研立项经费支持
作者: 胡中明：新疆工程学院能源工程学院，新疆 乌鲁木齐；魏鑫彤：新疆工程学院控制工程学院，新疆 乌鲁木齐；陈龙宇：新疆工程学院信息工程学院，新疆 乌鲁木齐；黄 达*, 朱 剑：新疆工程学院数理学院，新疆 乌鲁木齐
关键词: 合成网络结构；分层赋权图；综述；网络指标；Composite Network Structure； Layered Structured and Weighted Graph； Review； Network Index
摘要: 本文综述了复杂网络领域内，针对合成网络结构，特别是分层赋权图，所采用的一系列图指标及其在研究网络结构与动态特性中的最新进展。这些指标包括但不限于复杂网络的同步能力指标，用于评估网络在受到外部或内部扰动后恢复同步状态的能力；网络一致性指标，可以衡量带有扰动多智能体系统的抗干扰保持网络一致的能力；图的基尔霍夫指标，主要衡量电网络的电气传输效率；本文旨在总结这些指标在合成网络结构研究中的应用现状，探讨其相互关联与潜在影响，并展望未来的研究方向。
Abstract: This paper reviews a series of graphical indices applied to the composite network structures, particularly layered and weighted graphs, in the field of complex networks, as well as the latest progress of these network indices in studying network structure and dynamic characteristics. These indices include but not limited to the synchronization ability of complex networks, which is used to evaluate the network’s ability to resume a synchronized state after being disturbed by external or internal factors; The network coherence can measure the ability of a multi-agent system with disturbances to maintain network consistency against interference; and the Kirchhoff index of graphs, mainly measures the electrical transmission efficiency of an electrical network. This paper aims to summarize the current application status of these metrics in the research of synthetic network structures, explore their interrelationships and potential impacts, and look forward to future research directions.
文章引用：胡中明, 魏鑫彤, 陈龙宇, 黄达, 朱剑. 具有合成网络结构的分层赋权图指标综述[J]. 应用数学进展, 2025, 14(11): 193-198. https://doi.org/10.12677/aam.2025.1411475

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