The Immense Impact of Reverse Edges on Large Hierarchical Networks

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外文摘要：Hierarchical networks are frequently encountered in animal groups,gene networks,and artificial engi-neering systems such as multiple robots,unmanned vehicle systems,smart grids,wind farm networks,and so forth.The structure of a large directed hierarchical network is often strongly influenced by reverse edges from lower-to higher-level nodes,such as lagging birds'howl in a flock or the opinions of lower-level individuals feeding back to higher-level ones in a social group.This study reveals that,for most large-scale real hierarchical networks,the majority of the reverse edges do not affect the synchronization process of the entire network;the synchronization process is influenced only by a small part of these reverse edges along specific paths.More surprisingly,a single effective reverse edge can slow down the synchronization of a huge hierarchical network by over 60％.The effect of such edges depends not on the network size but only on the average in-degree of the involved subnetwork.The overwhelming majority of active reverse edges turn out to have some kind of"bunching"effect on the information flows of hierarchical networks,which slows down synchronization processes.This finding refines the current understanding of the role of reverse edges in many natural,social,and engineering hierarchical networks,which might be beneficial for precisely tuning the synchronization rhythms of these networks.Our study also proposes an effective way to attack a hierarchical network by adding a malicious reverse edge to it and provides some guidance for protecting a network by screening out the specific small proportion of vulnerable nodes.

外文关键词：

SynchronizabilityLarge hierarchical networksReverse edgesInformation flowsComplex networks

作者：

Haosen Cao、Bin-Bin Hu、Xiaoyu Mo、Duxin Chen、Jianxi Gao、Ye Yuan、Guanrong Chen、Tamás Vicsek、Xiaohong Guan、Hai-Tao Zhang

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作者单位：

MOE Engineering Research Center of Autonomous Intelligent Unmanned Systems,State Key Laboratory of Intelligent Manufacturing Equipment and Technology,School of Artificial Intelligence and Automation,Huazhong University of Science and Technology,Wuhan 430074,China

School of Mechanical and Aerospace Engineering,Nanyang Technological University,Singapore 639798,Singapore

Jiangsu Key Laboratory of Networked Collective Intelligence,School of Mathematics,Southeast University,Nanjing 210096,China

Department of Computer Science,Rensselaer Polytechnic Institute,Troy,NY 12180,USA

Department of Electronic Engineering,City University of Hong Kong,Hong Kong 999077,China

Department of Biological Physics,Eötvös University,Budapest 1117,Hungary

MOE Key Laboratory for Intelligent Networks and Network Security,School of Automation Science and Engineering,Xi'an Jiaotong University,Xi'an 710049,China

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基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Key Research and Development Program of ChinaGuangdong Basic and Applied Research FoundationScience and Technology Project of State Grid Corporation of China

项目编号：

62225306U214123552188102620031452022ZD01196012022B15151200695100-202199557A-0-5-ZN

出版年：

2024

DOI：

10.1016/j.eng.2023.06.011

工程(英文)

CSTPCDEI

ISSN：2095-8099

年,卷(期)：2024.36(5)