反向连边在大型分层网络中的影响（英文）

作     者：曹浩森 胡斌斌 莫小雨 陈都鑫 高建喜 袁烨 陈关荣 Tamás Vicsek 管晓宏 张海涛 

作者机构：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 School of Mechanical and Aerospace Engineering Nanyang Technological University Jiangsu Key Laboratory of Networked Collective Intelligence School of Mathematics Southeast University Department of Computer Science Rensselaer Polytechnic Institute Department of Electronic Engineering City University of Hong Kong Department of Biological Physics E?tv?s University MOE Key Laboratory for Intelligent Networks and Network Security School of Automation Science and Engineering Xi'an Jiaotong University 

出 版 物：《Engineering》 (工程(英文))

年 卷 期：2024年第5期

页      面：240-249页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported in part by the National Natural Science Foundation of China (62225306, U2141235, 52188102, and 62003145) the National Key Research and Development Program of China (2022ZD0119601) Guangdong Basic and Applied Research Foundation (2022B1515120069) the Science and Technology Project of State Grid Corporation of China (5100202199557A-0-5-ZN) 

摘      要：Hierarchical networks are frequently encountered in animal groups, gene networks, and artificial engineering 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 lowerlevel 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 ‘‘bunchingo 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.