2.793

2018影响因子

(CJCR)

  • 中文核心
  • EI
  • 中国科技核心
  • Scopus
  • CSCD
  • 英国科学文摘

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

复杂网络能控性鲁棒性研究进展

楼洋 李均利 李升 邓浩

楼洋, 李均利, 李升, 邓浩. 复杂网络能控性鲁棒性研究进展. 自动化学报, 2021, 45(x): 1−18 doi: 10.16383/j.aas.c200916
引用本文: 楼洋, 李均利, 李升, 邓浩. 复杂网络能控性鲁棒性研究进展. 自动化学报, 2021, 45(x): 1−18 doi: 10.16383/j.aas.c200916
Lou Yang, Li Jun-Li, Li Sheng, Deng Hao. Recent progress in controllability robustness of complex networks. Acta Automatica Sinica, 2021, 45(x): 1−18 doi: 10.16383/j.aas.c200916
Citation: Lou Yang, Li Jun-Li, Li Sheng, Deng Hao. Recent progress in controllability robustness of complex networks. Acta Automatica Sinica, 2021, 45(x): 1−18 doi: 10.16383/j.aas.c200916

复杂网络能控性鲁棒性研究进展

doi: 10.16383/j.aas.c200916
基金项目: 国家自然科学基金(62002249), 浙江大学CAD&CG国家重点实验室开放课题(A2112)资助
详细信息
    作者简介:

    楼洋:四川师范大学副研究员, 香港城市大学博士后. 2017年获得香港城市大学博士学位. 主要研究方向为复杂网络、进化算法和机器学习. 本文通信作者. E-mail: felix.lou@my.cityu.edu.hk

    李均利:四川师范大学研究员, 2002年获得浙江大学博士学位. 主要研究方向为图像处理、目标跟踪、智能计算. 本文通信作者. E-mail: li.junli@vip.163.com

    李升:四川师范大学硕士研究生. 主要研究方向为复杂网络

    邓浩:四川师范大学硕士研究生. 主要研究方向为进化计算, 复杂网络

Recent Progress in Controllability Robustness of Complex Networks

Funds: Supported by National Natural Science Foundation of P. R. China (62002249) and the Open Project Program of the State Key Lab of CAD&CG (A2112), Zhejiang University
More Information
    Author Bio:

    LOU Yang Associate Professor at Sichuan Normal University and Postdoctoral Fellow at City University of Hong Kong. He received his Ph.D. degree from City University of Hong Kong in 2017. His research interests include complex networks, evolutionary computation, and machine learning. Corresponding author of this paper

    LI Jun-Li Professor at Sichuan Normal University. He received his Ph.D. degree from Zhejiang University in 2002. His research interests include image processing, target tracking, and computational intelligence. Corresponding author of this paper

    LI Sheng Master student of Sichuan Normal University. His research interest covers complex networks

    DENG Hao Master student of Sichuan Normal University. His research interest covers evolutionary computing and complex networks

  • 摘要: 研究复杂网络能控性鲁棒性对包括社会网络、生物和技术网络等在内的复杂系统的控制和应用具有重要价值. 复杂网络的能控性是指: 可通过若干控制节点和适当的输入, 在有限时间内将系统状态驱动至任意目标状态. 能控性鲁棒性则是指在受到攻击的情况下, 复杂网络依然维持能控性的能力. 设计具有优异能控性鲁棒性的复杂网络模型和优化实际网络的能控性鲁棒性一直是复杂网络领域的重要研究内容. 本文首先比较了常用的能控性鲁棒性定义及度量, 接着从攻击策略的角度分析了三类攻击的特点及效果, 包括随机攻击、基于特征的蓄意攻击和启发式攻击. 然后比较了常见模型网络的能控性鲁棒性. 介绍了常用优化策略, 包括模型设计和重新连边等. 目前的研究在攻击策略和拓扑结构优化方面都取得了进展, 也为进一步理论分析提供条件. 最后总结全文并提出潜在研究方向.
  • 图  1  匹配和节点控制中心性的例子.

    Fig.  1  Examples of matching and node control centrality.

    图  2  按文献[57]连边分类举例.

    Fig.  2  An example of edge classification according to Ref. [57].

    图  3  按文献[57]节点分类举例.

    Fig.  3  An example of node classification according to Ref. [57].

    图  4  能控性鲁棒性度量方式比较举例.

    Fig.  4  Comparison of two different controllability robustness measurements.

    图  5  能控性鲁棒性与连通性鲁棒性.

    Fig.  5  Controllability robustness and connectedness robustness.

    图  6  关键连边和关键节点在遭受攻击过程中变化.

    Fig.  6  Key edges and nodes may change during attacks.

    图  7  常见的网络模型在攻击下的能控性曲线变化.

    Fig.  7  The controllability curves of 9 network topologies under 4 different attack strategies.

    图  8  所有$ N $节点和$ M $连边网络, 满足ENC的网络, 全齐网络, 以及最优网络之间的关系图.

    Fig.  8  The relationship diagram of the $ N $-node $ M $-edge networks, ENC networks, totally homogeneous networks, and the optimal networks.

    表  1  常用能控性鲁棒性优化策略的优点与不足.

    Table  1  Pros and cons of the strategies for controllability robustness optimization.

    优点不足
    模型优化设计基于特定理论, 模型简单易实现
    (比如同余论[122]、Henneberg[106]理论)
    容易受理论约束 (比如同余论限制生成网络的度数不能任意调整)
    重新连边根据实际需求, 对网络结构做一定范围的调整具有一定的随机性, 且通常需要较大的计算量
    全齐网络经验上的能控性鲁棒性最优结构通常不符合实际网络特征与需求 (比如
    交通网络无法设计为全齐网络)
    模体在优化设计或重新连边过程中, 刻意增加网络中特定模体的数量不同模体对能控性鲁棒性的理论价值和意义有待进一步理清
    下载: 导出CSV

    表  2  能控性鲁棒性优化的网络结构.

    Table  2  Comparison of network topologies with optimized controllability robustness.

    优化设计重新连边全齐网络模体
    MCN
    QSN
    QSNR
    RTN
    RRN
    EH
    下载: 导出CSV
  • [1] Barabasi A-L. Network science. Cambridge University Press, 2016.
    [2] Newman M E. Networks: an introduction. Oxford University Press, 2010
    [3] Chen G, Wang X, Li X. Fundamentals of complex networks: models, structures and dynamics. (2 Edn) John Wiley & Sons, 2014
    [4] 汪小帆, 李翔, 陈关荣. 复杂网络理论及其应用. 清华大学出版社, 2006.

    Wang Xiao-Fan, Li Xiang, Chen Guan-Rong. Complex network theory and its applications. Tsinghua University Press, 2006
    [5] Chen D, Shao Q, Liu Z, Yu W, Chen C L P. Ridesourcing behavior analysis and prediction: a network perspective. IEEE Transactions on Intelligent Transportation Systems, 2020(doi: 10.1109/TITS.2020.3023951)
    [6] Chen G, Lou Y. Naming game: models, simulations and analysis. Springer, 2019
    [7] Ding Y. Scientific collaboration and endorsement: network analysis of coauthorship and citation networks. Journal of Informetrics, 2011, 5(1): 187−203 doi: 10.1016/j.joi.2010.10.008
    [8] Davis K F, D’Odorico P, Laio F, Ridolfi L. Global spatio-temporal patterns in human migration: a complex network perspective. PLOS ONE, 2013, 8: e53723 doi: 10.1371/journal.pone.0053723
    [9] 熊熙, 乔少杰, 吴涛, 吴越, 韩楠, 张海清. 基于时空特征的社交网络情绪传播分析与预测模型. 自动化学报, 2018, 44(12): 2290−2299

    Xiong Xi, Qiao Shao-Jie, Wu Tao, Wu Yue, Han Nan, Zhang Hai-Qing. Spatio-temporal feature based emotional contagion analysis and prediction model for online social networks. Acta Automatica Sinica, 2018, 44(12): 2290−2299
    [10] Lou Y, Chen G. Analysis of the “naming game” with learning errors in communications. Scientific Reports, 2015, 5: 12191 doi: 10.1038/srep12191
    [11] Lou Y, Chen G, Hu J. Communicating with sentences: a multi-word naming game model. Physica A: Statistical Mechanics and Its Applications, 2018, 490: 857−868 doi: 10.1016/j.physa.2017.08.066
    [12] Lou Y, Chen G, Fan Z, Xiang L. Local communities obstruct global consensus: naming game on multi-local-world networks. Physica A: Statistical Mechanics and Its Applications, 2018, 492: 1741−1752 doi: 10.1016/j.physa.2017.11.094
    [13] 黄春林, 刘兴武, 邓明华, 周杨, 卜东波. 复杂网络上疾病传播溯源算法综述. 计算机学报, 2017, 40(5): 1−28

    Huang Chun-Lin, Liu Xing-Wu, Deng Ming-Hua, Zhou Yang, Bu Dong-Bo. A survey on algorithms for epidemic source identification on complex networks. Chinese Journal of Computers, 2017, 40(5): 1−28
    [14] Kabir K A, Kuga K, Tanimoto J. Analysis of SIR epidemic model with information spreading of awareness. Chaos, Solitons & Fractals, 2019, 119: 118−125
    [15] Firth J A, Hellewell J, Klepac P, Kissler S, Kucharski A J, Spurgin L G. Using a real-world network to model localized Covid-19 control strategies. Nature Medicine, 2020, 26: 1616−1622 doi: 10.1038/s41591-020-1036-8
    [16] Zhang Y, Wu G, Liu X, Yu W, Chen D. Maximum Markovian order detection for collective behavior. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020, 30: 083121 doi: 10.1063/5.0008397
    [17] Chen D, Liu X, Xu B, Zhang H T. Intermittence and connectivity of interactions in pigeon flock flights. Scientific Reports, 2017, 7: 10452 doi: 10.1038/s41598-017-09986-5
    [18] Liu Y-Y, Slotine J-J, Barabasi A-L. Controllability of complex networks. Nature, 2011, 473: 167−173 doi: 10.1038/nature10011
    [19] Wang W-X, Ni X, Lai Y-C, Grebogi C. Optimizing controllability of complex networks by minimum structural perturbations. Physical Review E, 2012, 85: 026115 doi: 10.1103/PhysRevE.85.026115
    [20] Yuan Z, Zhao C, Di Z, Wang W-X, Lai Y-C. Exact controllability of complex networks. Nature Communications, 2013, 4: 2447 doi: 10.1038/ncomms3447
    [21] Posfai M, Liu Y-Y, Slotine J-J, Barabasi A-L. Effect of correlations on network controllability. Scientific Reports, 2013, 3: 1067 doi: 10.1038/srep01067
    [22] Menichetti G, Dall’Asta L, Bianconi G. Network controllability is determined by the density of low in-degree and out-degree nodes. Physical Review Letters, 2014, 113: 078701 doi: 10.1103/PhysRevLett.113.078701
    [23] 周涛, 张子柯, 陈关荣, 汪小帆, 史定华, 狄增如, 樊瑛, 方锦清, 韩筱璞, 刘建国, 刘润然, 刘宗华, 陆君安, 吕金虎, 吕琳媛, 荣智海, 汪秉宏, 许小可, 章忠志. 复杂网络研究的机遇与挑战. 电子科技大学学报, 2014, 43(1): 1−5

    Zhou Tao, Zhang Zi-Ke, Chen Guan-Rong, Wang Xiao-Fan, Shi Ding-Hua, Di Zeng-Ru, Fan Ying, Fang Jin-Qing, Han Xiao-Pu, Liu Jian-Guo, Liu Run-Ran, Liu Zong-Hua, Lu Jun-An, Lü Jin-Hu, Lü Lin-Yuan, Rong Zhi-Hai, Wang Bing-Hong, Xu Xiao-Ke, Zhang Zhong-Zhi. The opportunities and challenges of complex networks research. Journal of University of Electronic Science and Technology of China, 2014, 43(1): 1−5
    [24] 侯绿林, 老松杨, 肖延东, 白亮. 复杂网络可控性研究现状综述. 物理学报, 2015, 64(18): 188901 doi: 10.7498/aps.64.188901

    Hou Lü-Lin, Lao Song-Yang, Xiao Yan-Dong, Bai Liang. Recent progress in controllability of complex network. Acta Physica Sinica, 2015, 64(18): 188901 doi: 10.7498/aps.64.188901
    [25] 聂森, 复杂网络可控性研究, 中国科学技术大学, 2015

    Nie Sen. Research on Controllability of Complex Networks. Ph.D.thesis, [Ph. D. dissertation], University of Science and Technology of China, 2015
    [26] Motter A E. Networkcontrology. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015, 25: 097621 doi: 10.1063/1.4931570
    [27] Wang L, Wang X, Chen G, Tang W K S. Controllability of networked MIMO systems. Automatica, 2016, 69: 405−409 doi: 10.1016/j.automatica.2016.03.013
    [28] Liu Y-Y, Barabasi A-L. Control principles of complex systems. Review of Modern Physics, 2016, 88: 035006 doi: 10.1103/RevModPhys.88.035006
    [29] Wang L, Wang X, Chen G. Controllability of networked higher-dimensional systems with one-dimensional communication. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017, 375: 20160215 doi: 10.1098/rsta.2016.0215
    [30] Wang L-Z, Chen Y-Z, Wang W-X, Lai Y-C. Physical controllability of complex networks. Scientific Reports, 2017, 7: 40198 doi: 10.1038/srep40198
    [31] Zhang Y, Zhou T. Controllability analysis for a networked dynamic system with autonomous subsystems. IEEE Transactions on Automatic Control, 2016, 62: 3408−3415
    [32] Xiang L, Chen F, Ren W, Chen G. Advances in network controllability. IEEE Circuits and Systems Magazine, 2019, 19: 8−32 doi: 10.1109/MCAS.2019.2909446
    [33] 段广仁. 高阶系统方法-Ⅱ. 能控性与全驱性. 自动化学报, 2020, 46(8): 1571−1581

    Duan Guang-Ren. High-order system approaches: Ⅱ. Controllability and full-actuation. Acta Automatica Sinica, 2020, 46(8): 1571−1581
    [34] Chen, G. Pinning control and synchronization on complex dynamical networks. International Journal of Control, Automation and Systems, 2014, 12: 221−230 doi: 10.1007/s12555-014-9001-2
    [35] Holme P, Kim B J, Yoon C N, Han S K. Attack vulnerability of complex networks. Physical Review E, 2002, 65: 056109 doi: 10.1103/PhysRevE.65.056109
    [36] Shargel B, Sayama H, Epstein I R, Bar-Yam Y. Optimization of robustness and connectivity in complex networks. Physical Review Letters, 2003, 90: 068701 doi: 10.1103/PhysRevLett.90.068701
    [37] Schneider C M, Moreira A A, Andrade J S, Havlin S, Herrmann H J. Mitigation of malicious attacks on networks. Proceedings of the National Academy of Sciences, 2011, 108: 3838−3841 doi: 10.1073/pnas.1009440108
    [38] Liu Y-Y, Slotine J-J, Barabasi A-L. Control centrality and hierarchical structure in complex networks. PLOS ONE, 2012, 7: e44459 doi: 10.1371/journal.pone.0044459
    [39] Bashan A, Berezin Y, Buldyrev S, Havlin S. The extreme vulnerability of interdependent spatially embedded networks. Nature Physics, 2013, 9: 667−672 doi: 10.1038/nphys2727
    [40] Xiao Y-D, Lao S-Y, Hou L-L, Bai L. Optimization of robustness of network controllability against malicious attacks. Chinese Physics B, 2014, 23: 118902 doi: 10.1088/1674-1056/23/11/118902
    [41] 李文锋, 符修文. 无线传感器网络抗毁性. 计算机学报, 2015, 38(3): 625−647

    Li Wen-Feng, Fu Xiu-Wen. Survey on invulnerability of wireless sensor networks. Chinese Journal of Computers, 2015, 38(3): 625−647
    [42] 董政呈, 方彦军, 田猛. 相互依存网络抗毁性研究综述. 复杂系统与复杂性科学, 2017, 14(3): 30−44

    Dong Zhengcheng, Fang Yanjun, Tian Meng. Review on invulnerability of interdependent networks. complex systems and complexity science. Complex Systems and Complexity Science, 2017, 14(3): 30−44
    [43] 王尔申, 王玉伟, 庞涛, 曲萍萍, 姜毅. 基于边攻击成本的复杂网络鲁棒性研究. 电子学报, 2018, 46(5): 1166−1172

    Wang Er-Shen, Wang Yu-Wei, Pang Tao, Qu Ping-Ping, Jiang Yi. Research on robustness of complex networks with edge’s attack cost. Acta Electronica Sinica, 2018, 46(5): 1166−1172
    [44] 赵志刚, 周根贵, 杜辉. 复杂加权供应链网络级联抗毁性研究. 小型微型计算机系统, 2019, 40(12): 2591−2596

    Zhao Zhi-Gang, Zhou Gen-Gui, Du Hui. Research on cascading invulnerability of complex weighted supply chain networks. Journal of Chinese Computer Systems, 2019, 40(12): 2591−2596
    [45] 王哲, 李建华, 康东, 冉淏丹. 复杂网络鲁棒性增强策略研究综述. 复杂系统与复杂性科学, 2020, 17(3): 1−26

    Wang Zhe, Li Jianhua, Kang Dong, Ran Haodan. Review on strategies enhancing the robustness of complex network. Complex Systems and Complexity Science, 2020, 17(3): 1−26
    [46] Yan G, Vertes P E, Towlson E K, Chew Y L, Walker D S, Schafer W R, Barabasi A-L. Network control principles predict neuron function in the Caenorhabditis elegans connectome. Nature, 2017, 550: 519−523 doi: 10.1038/nature24056
    [47] Liu J, Zhou M, Wang S, Liu P. A comparative study of network robustness measures. Frontiers of Computer Science, 2017, 11: 568−584 doi: 10.1007/s11704-016-6108-z
    [48] 谭跃进, 吴俊, 邓宏钟. 复杂网络抗毁性研究进展. 上海理工大学学报, 2011, 33(6): 653−668

    Tan Yue-Jin, Wu Jun, Deng Hong-Zhong. Progress in invulnerability of complex networks. Journal of University of Shanghai for Science and Technology, 2011, 33(6): 653−668
    [49] Yamashita K, Yasuda Y, Nakamura R, Ohsaki H. On the predictability of network robustness from spectral measures. In: Proceedings of the IEEE Annual Computer Software and Applications Conference (COMPSAC), 2019, 24−29
    [50] Chen G, Lou Y, Wang L. A comparative study on controllability robustness of complex networks. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, 2019, 66: 828−832 doi: 10.1109/TCSII.2019.2908435
    [51] Li X, Zhang Z, Liu J, Gai K. A new complex network robustness attack algorithm. In: Proceedings of the 2019 ACM International Symposium on Blockchain and Secure Critical Infrastructure, 2019, 13−17
    [52] Lou Y, He Y, Wang L, Chen G. Predicting network controllability robustness: A convolutional neural network approach. IEEE Transactions on Cybernetics, 2020(doi: 10.1109/TCYB.2020.3013251)
    [53] Fan C, Zeng L, Sun Y, Liu Y-Y. Finding key players in complex networks through deep reinforcement learning. Nature Machine Intelligence, 2020, 2: 317−324 doi: 10.1038/s42256-020-0177-2
    [54] Kalman R E. On the general theory of control systems. In: Proceedings First International Conference on Automatic Control, 1960. 481−492
    [55] Ding J, Lu Y-Z. Control backbone: an index for quantifying a nodes importance for the network controllability. Neurocomputing, 2015, 153: 309−318 doi: 10.1016/j.neucom.2014.11.024
    [56] Hosoe S. Determination of generic dimensions of controllable subspaces and its application. IEEE Transactions on Automatic Control, 1980, 25: 1192−1196 doi: 10.1109/TAC.1980.1102506
    [57] Lou Y, Wang L, Chen G. A framework of hierarchical attacks to network controllability. Communications in Nonlinear Science and Numerical Simulation, 2021(to be published)
    [58] Usman U, Mahmood A, Wang L. Robust control centrality. In: Proceedings of the 2019 Chinese Control Conference, 2019, 5486−5491
    [59] Annamalai C. Finding perfect matchings in bipartite hypergraphs. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2016, 1814−1823
    [60] Williams V V. Multiplying matrices faster than Coppersmith-Winograd. In: Proceedings of the ACM Symposium on Theory of Computing, 2012, 887−898
    [61] Sun P, Kooij R E, He Z, Van Mieghem P. Quantifying the robustness of network controllability. In: Proceedings of International Conference on System Reliability and Safety (ICSRS), 2019. 66−76
    [62] 林景栋, 吴欣怡, 柴毅, 尹宏鹏. 卷积神经网络结构优化综述. 自动化学报, 2020, 46(1): 24−37

    Lin Jing-Dong, Wu Xin-Yi, Chai Yi, Yin Hong-Peng. Structure optimization of convolutional neural networks: a survey. Acta Automatica Sinica, 2020, 46(1): 24−37
    [63] Lou Y, He Y, Wang L, Tsang K F, Chen G. Knowledge-based prediction of network controllability robustness. arXiv preprint, 2020, arXiv: 2003.08563
    [64] Lou Y, He Y, Wang L, Tsang K F, Chen G. Predicting the robustness of undirected network controllability. In: Proceedings of the 39th Chinese Control Conference, 2020, 4550−4553
    [65] Chan H, Akoglu L. Optimizing network robustness by edge rewiring: a general framework. Data Mining and Knowledge Discovery, 2016, 30(5): 1395−1425 doi: 10.1007/s10618-015-0447-5
    [66] Yan G, Martinez N D, Liu Y-Y. Degree heterogeneity and stability of ecological networks. Journal of the Royal Society Interface, 2017, 14(131): 20170189 doi: 10.1098/rsif.2017.0189
    [67] Wang S, Liu J, Jin Y. Surrogate-assisted robust optimization of large-scale networks based on graph embedding. IEEE Transactions on Evolutionary Computation, 2020, 24(4): 735−749 doi: 10.1109/TEVC.2019.2950935
    [68] Ruan Y-R, Lao S-Y, Wang J-D, Bai L, Chen L-D. Node importance measurement based on neighborhood similarity in complex network. Acta Physica Sinica, 2017, 66: 038902 doi: 10.7498/aps.66.038902
    [69] Simon M, Luptakova D I, Huraj L, Hostovecky M, Pospichal J. Combined heuristic attack strategy on complex networks. Mathematical Problems in Engineering, 2017, 2017: 6108563
    [70] Yang H, An S. Critical nodes identification in complex networks. Symmetry, 2020, 12: 123 doi: 10.3390/sym12010123
    [71] Wu-Yan E, Betzel R F, Tang E, Gu S, Pasqualetti F, Bassett D S. Benchmarking measures of network controllability on canonical graph models. Journal of Nonlinear Science, 2018, 30: 2195−2233
    [72] Zhang R, Wang X, Cheng M, Jia T. The evolution of network controllability in growing networks. Physica A: Statistical Mechanics and Its Applications, 2019, 520: 257−266 doi: 10.1016/j.physa.2019.01.042
    [73] Hao Y, Duan Z, Chen G. Further on the controllability of networked MIMO LTI systems. International Journal of Robust and Nonlinear Control, 2018, 28: 1778−1788 doi: 10.1002/rnc.3986
    [74] Brohl T, Lehnertz K. Centrality-based identification of important edges in complex networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019, 29: 033115 doi: 10.1063/1.5081098
    [75] Thomas J, Ghosh S, Parek D, Ruths D, Ruths J. Robustness of network controllability to degree-based edge attacks. In International Workshop on Complex Networks and their Applications, Springer, 2016. 525−537
    [76] Nie T, Guo Z, Zhao K, Lu Z-M. New attack strategies for complex networks. Physica A: Statistical Mechanics and Its Applications, 2015, 424: 248−253 doi: 10.1016/j.physa.2015.01.004
    [77] Nguyen Q, Pham H, Cassi D, Bellingeri M. Conditional attack strategy for real-world complex networks. Physica A: Statistical Mechanics and Its Applications, 2019, 530: 121561 doi: 10.1016/j.physa.2019.121561
    [78] Gao Y-L, Chen S-M, Nie S, Ma F, Guan J-J. Robustness analysis of interdependent networks under multiple-attacking strategies. Physica A: Statistical Mechanics and Its Applications, 2018, 496: 495−504 doi: 10.1016/j.physa.2017.12.085
    [79] Hao Y, Jia L, Wang Y. Edge attack strategies in interdependent scale-free networks. Physica A: Statistical Mechanics and Its Applications, 2020, 540: 122759 doi: 10.1016/j.physa.2019.122759
    [80] Huang X, Gao J, Buldyrev S V, Havlin S, Stanley H E. Robustness of interdependent networks under targeted attack. Physical Review E, 2011, 83: 065101 doi: 10.1103/PhysRevE.83.065101
    [81] Dong G, Gao J, Tian L, Du R, He Y. Percolation of partially interdependent networks under targeted attack. Physical Review E, 2012, 85: 016112 doi: 10.1103/PhysRevE.85.016112
    [82] Cui P, Zhu P, Wang K, Xun P, Xia Z. Enhancing robustness of interdependent network by adding connectivity and dependence links. Physica A: Statistical Mechanics and Its Applications, 2018, 497: 185−197 doi: 10.1016/j.physa.2017.12.142
    [83] Dong G, Gao J, Du R, Tian L, Stanley H E, Havlin S. Robustness of network of networks under targeted attack. Physical Review E, 2013, 87: 052804 doi: 10.1103/PhysRevE.87.052804
    [84] Liu X, Peng H, Gao J. Vulnerability and controllability of networks of networks. Chaos, Solitons & Fractals, 2015, 80: 125−138
    [85] Bellingeri M, Cassi D. Robustness of weighted networks. Physica A: Statistical Mechanics and Its Applications, 2018, 489: 47−55 doi: 10.1016/j.physa.2017.07.020
    [86] Pu C-L, Pei W-J, Michaelson A. Robustness analysis of network controllability. Physica A: Statistical Mechanics and Its Applications, 2012, 391: 4420−4425 doi: 10.1016/j.physa.2012.04.019
    [87] Lu Z-M, Li X-F. Attack vulnerability of network controllability. PLOS ONE, 2016, 11: e0162289 doi: 10.1371/journal.pone.0162289
    [88] Li X, Chen G. A local-world evolving network model. Physica A: Statistical Mechanics and Its Applications, 2003, 328: 274−286 doi: 10.1016/S0378-4371(03)00604-6
    [89] Fan Z, Chen G, Zhang Y. A comprehensive multi-local-world model for complex networks. Physics Letters A, 2009, 373: 1601−1605 doi: 10.1016/j.physleta.2009.02.072
    [90] Sun S, Ma Y, Wu Y, Wang L, Xia C. Towards structural controllability of local-world networks. Physics Letters A, 2016, 380: 1912−1917 doi: 10.1016/j.physleta.2016.03.048
    [91] Nie S, Wang X, Zhang H, Li Q, Wang B. Robustness of controllability for networks based on edge-attack. PLOS ONE, 2014, 9: e89066 doi: 10.1371/journal.pone.0089066
    [92] Wang H, Huang J, Xu X, Xiao Y. Damage attack on complex networks. Physica A: Statistical Mechanics and Its Applications, 2014, 408: 134−148 doi: 10.1016/j.physa.2014.04.001
    [93] Requiao da Cunha B, Gonzalez-Avella J C, Goncalves S. Fast fragmentation of networks using module-based attacks. PLOS ONE, 2015, 10: e0142824 doi: 10.1371/journal.pone.0142824
    [94] Shai S, Kenett D Y, Kenett Y N, Faust M, Dobson S, Havlin S. Critical tipping point distinguishing two types of transitions in modular network structures. Physical Review E, 2015, 92: 062805 doi: 10.1103/PhysRevE.92.062805
    [95] Ma L, Liu J, Duan B. Evolution of network robustness under continuous topological changes. Physica A: Statistical Mechanics and Its Applications, 2016, 451: 623−631 doi: 10.1016/j.physa.2016.01.088
    [96] Zhang X, Wu J, Wang H, Xiong J, Yang K. Optimization of disintegration strategy for multi-edges complex networks. In: Proceedings of the 2016 IEEE Congress on Evolutionary Computation (CEC), IEEE, 2016. 522−528
    [97] 孙昱, 姚佩阳, 张杰勇, 付凯. 基于优化理论的复杂网络节点攻击策略. 电子与信息学报, 2017, 39(3): 518−524

    Sun Yu, Yao Peiyang, Zhang Jieyong, Fu Kai. Node attack strategy of complex networks based on optimization theory. Journal of Electronics and Information Technology, 2017, 39(3): 518−524
    [98] Ventresca M. Global search algorithms using a combinatorial unranking-based problem representation for the critical node detection problem. Computers & Operations Research, 2012, 39: 2763−2775
    [99] Deng Y, Wu J, Tan Y-J. Optimal attack strategy of complex networks based on tabu search. Physica A: Statistical Mechanics and Its Applications, 2016, 442: 74−81 doi: 10.1016/j.physa.2015.08.043
    [100] Qi M, Deng Y, Deng H, Wu J. Optimal disintegration strategy in multiplex networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018, 28: 121104 doi: 10.1063/1.5078449
    [101] Lozano M, Garcia-Martinez C, Rodriguez F J, Trujillo H M. Optimizing network attacks by artificial bee colony. Information Sciences, 2017, 377: 30−50 doi: 10.1016/j.ins.2016.10.014
    [102] Li Q, Liu S-Y, Yang X-S. Neighborhood information-based probabilistic algorithm for network disintegration. Expert Systems with Applications, 2020, 139: 112853 doi: 10.1016/j.eswa.2019.112853
    [103] Erdos P, Renyi A. On the evolution of random graphs. Mathematical Institute of the Hungarian Academy of Sciences, 1960, 5: 17−61
    [104] Newman M E, Watts D J. Renormalization group analysis of the small-world network model. Physics Letters A, 1999, 263: 341−346 doi: 10.1016/S0375-9601(99)00757-4
    [105] Watts D J, Strogatz S H. Collective dynamics of ‘small-world’ networks. Nature, 1998, 393: 440−442 doi: 10.1038/30918
    [106] Yang D, Liu M, Zhang Y, Lin D, Fan Z, Chen G. Henneberg growth of social networks: modeling the Facebook. IEEE Transactions on Network Science and Engineering, 2020, 7: 701−712 doi: 10.1109/TNSE.2018.2856280
    [107] Goh K-I, Kahng B, Kim D. Universal behavior of load distribution in scale-free networks. Physical Review Letters, 2001, 87: 278701 doi: 10.1103/PhysRevLett.87.278701
    [108] Sorrentino F. Effects of the network structural properties on its controllability. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007, 17: 033101 doi: 10.1063/1.2743098
    [109] Herrmann H J, Schneider C M, Moreira A A, Andrade J S, Havlin, S. Onion-like network topology enhances robustness against malicious attacks. Journal of Statistical Mechanics: Theory and Experiment, 2011, 2011: P01027
    [110] Wu Z-X, Holme P. Onion structure and network robustness. Physical Review E, 2011, 84: 026106 doi: 10.1103/PhysRevE.84.026106
    [111] Tanizawa T, Havlin S, Stanley H E. Robustness of onionlike correlated networks against targeted attacks. Physical Review E, 2012, 85: 046109 doi: 10.1103/PhysRevE.85.046109
    [112] Hayashi Y, Uchiyama N. Onion-like networks are both robust and resilient. Scientific Reports, 2018, 8: 11241 doi: 10.1038/s41598-018-29626-w
    [113] Lou Y, Wang L, Chen G. Toward stronger robustness of network controllability: A snapback network model. IEEE Transactions on Circuits and Systems I: Regular Papers, 2018, 65: 2983−2991 doi: 10.1109/TCSI.2018.2821124
    [114] Lou Y, Wang L, Chen G. Local diversity-stability of the q-snapback network model. Physica A: Statistical Mechanics and Its Applications, 2019, 536: 121020 doi: 10.1016/j.physa.2019.04.256
    [115] Lou Y, Wang L, Chen G. Enhancing controllability robustness of q-snapback networks through redirecting edges. Research, 2019, 2019: 7857534
    [116] Lou Y, Wang L, Tsang K-F, Chen G. Towards optimal robustness of network controllability: An empirical necessary condition. IEEE Transactions on Circuits and Systems I: Regular Papers, 2020, 67(9): 3163−3174 doi: 10.1109/TCSI.2020.2986215
    [117] Eiben A E, Smith J. From evolutionary computation to the evolution of things. Nature, 2015, 521: 476−482 doi: 10.1038/nature14544
    [118] 丁青锋, 尹晓宇. 差分进化算法综述. 智能系统学报, 2017, 12(4): 431−442

    Ding Qingfeng, Yin Xiaoyu. Research survey of differential evolution algorithms. CAAI Transactions on Intelligent Systems, 2017, 12(4): 431−442
    [119] Lou Y, Xie S, Chen G. Searching Better Rewiring Strategies and Objective Functions for Stronger Controllability Robustness. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, 2020(doi: 10.1109/TCSII.2020.3047538)
    [120] 林诗洁, 董晨, 陈明志, 张凡, 陈景辉. 新型群智能优化算法综述. 计算机工程与应用, 2018, 54(12): 1−9

    Lin Shijie, Dong Chen, Chen Mingzhi, Zhang Fan, Chen Jinghui. Summary of new group intelligent optimization algorithms. Computer Engineering and Applications, 2018, 54(12): 1−9
    [121] Lou Y, Yuen S Y, Chen G. Non-revisiting stochastic search revisited: results, perspectives, and future directions. Swarm and Evolutionary Computation, 2021, 61: 100828 doi: 10.1016/j.swevo.2020.100828
    [122] Yan X-Y, Wang W-X, Chen G, Shi D-H. Multiplex congruence network of natural numbers. Scientific Reports, 2016, 6: 23714 doi: 10.1038/srep23714
    [123] Bai L, Xiao Y-D, Hou L-L, Lao S-Y. Smart rewiring: Improving network robustness faster. Chinese Physics Letters, 2015, 32: 078901 doi: 10.1088/0256-307X/32/7/078901
    [124] Wu J, Barahona M, Tan Y-J, Deng H-Z. Natural connectivity of complex networks. Chinese Physics Letters, 2010, 27: 078902 doi: 10.1088/0256-307X/27/7/078902
    [125] Chakrabarti D, Wang Y, Wang C, Leskovec J, Faloutsos C. Epidemic thresholds in real networks. ACM Transactions on Information and System Security (TISSEC), 2008, 10(4): 1−26
    [126] Estrada E, Hatano N, Benzi M. The physics of communicability in complex networks. Physics Reports, 2012, 514: 89−119 doi: 10.1016/j.physrep.2012.01.006
    [127] Fiedler M. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 1973, 23: 298−305 doi: 10.21136/CMJ.1973.101168
    [128] Ghosh A, Boyd S, Saberi A. Minimizing effective resistance of a graph. SIAM Review, 2008, 50: 37−66 doi: 10.1137/050645452
    [129] Wu J, Barahona M, Tan Y-J, Deng H-Z. Spectral measure of structural robustness in complex networks. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2011, 41(6): 1244−1252 doi: 10.1109/TSMCA.2011.2116117
    [130] Xiao S, Xiao G, Cheng T H, Ma S, Fu X, Soh H. Robustness of scale-free networks under rewiring operations. EPL (Europhysics Letters), 2010, 89: 38002 doi: 10.1209/0295-5075/89/38002
    [131] Newman M E. Mixing patterns in networks. Physical Review E, 2003, 67: 026126 doi: 10.1103/PhysRevE.67.026126
    [132] Louzada V H, Daolio F, Herrmann H J, Tomassini M. Smart rewiring for network robustness. Journal of Complex Networks, 2013, 1(2): 150−159 doi: 10.1093/comnet/cnt010
    [133] Buesser P, Daolio F, Tomassini M. Optimizing the robustness of scale-free networks with simulated annealing. In: Proceedings of the International Conference on Adaptive and Natural Computing Algorithms, Springer, 2011. 167−176
    [134] Zhou M, Liu J. A memetic algorithm for enhancing the robustness of scale-free networks against malicious attacks. Physica A: Statistical Mechanics and Its Applications, 2014, 410: 131−143 doi: 10.1016/j.physa.2014.05.002
    [135] Zeng A, Liu W. Enhancing network robustness against malicious attacks. Physical Review E, 2012, 85: 066130 doi: 10.1103/PhysRevE.85.066130
    [136] Liu J, Abbass H A, Tan K C. Evolving robust networks using evolutionary algorithms. In Evolutionary Computation and Complex Networks, Springer, 2019. 117−140
    [137] Wang S, Liu J. Designing comprehensively robust networks against intentional attacks and cascading failures. Information Sciences, 2019, 478: 125−140 doi: 10.1016/j.ins.2018.11.005
    [138] Gunasekara R C, Mohan C K, Mehrotra K. Multi-objective optimization to improve robustness in networks. In MultiObjective Optimization, Springer, 2018. 115−139
    [139] Hou L, Lao S, Jiang B, Bai L. Enhancing complex network controllability by rewiring links. In: Proceedings of the International Conference on Intelligent System Design and Engineering Applications (ISDEA), 2013. 709−711
    [140] Xu J, Wang J, Zhao H, Jia S. Improving controllability of complex networks by rewiring links regularly. In: Proceedings of Chinese Control and Decision Conference (CCDC), 2014. 642−645
    [141] Wang S, Liu J. A multi-objective evolutionary algorithm for promoting the emergence of cooperation and controllable robustness on directed networks. IEEE Transactions on Network Science and Engineering, 2018, 5(2): 92−100 doi: 10.1109/TNSE.2017.2742522
    [142] Hou L, Lao S, Small M, Xiao Y. Enhancing complex network controllability by minimum link direction reversal. Physics Letters A, 2015, 379: 1321−1325 doi: 10.1016/j.physleta.2015.03.018
    [143] Shi D, Lu L, Chen G. Totally homogeneous networks. National Science Review, 2019, 6: 962−969 doi: 10.1093/nsr/nwz050
    [144] Shi D, Chen G, Thong W W K, Yan X. Searching for optimal network topology with best possible synchronizability. IEEE Circuits and Systems Magazine, 2013, 13(1): 66−75 doi: 10.1109/MCAS.2012.2237145
    [145] Fan T, Lu L, Shi D. Towards the cycle structures in complex network: a new perspective. arXiv preprint, 2019, arXiv: 1903.01397
    [146] Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U. Network motifs: simple building blocks of complex networks. Science, 2002, 298: 824−827 doi: 10.1126/science.298.5594.824
    [147] Menck P J, Heitzig J, Kurths J, Schellnhuber H J. How dead ends undermine power grid stability. Nature Communications, 2014, 5: 1−8
    [148] Gorochowski T E, Grierson C S, Bernardo M. Organization of feed-forward loop motifs reveals architectural principles in natural and engineered networks. Science Advances, 2018, 4(3): eaap9751 doi: 10.1126/sciadv.aap9751
    [149] Badhwar R, Bagler G. Robust sigmoidal control response of C. elegans neuronal network. In International Joint Conference on Rough Sets, Springer, 2017. 393−402
    [150] Dey A K, Gel Y R, Poor H V. What network motifs tell us about resilience and reliability of complex networks. Proceedings of the National Academy of Sciences, 2019, 116(39): 19368−19373 doi: 10.1073/pnas.1819529116
    [151] 贾承丰, 韩华, 完颜娟, 吕亚楠. 基于网络模体特征攻击的网络抗毁性研究. 复杂系统与复杂性科学, 2017, 14(4): 43−50

    Jia Chengfeng, Han Hua, Wanyan Juan, Lu Yanan. Network destruction resistance based on network motif feature. Complex Systems and Complexity Science, 2017, 14(4): 43−50
  • 加载中
计量
  • 文章访问数:  422
  • HTML全文浏览量:  472
  • 被引次数: 0
出版历程
  • 网络出版日期:  2021-03-17

目录

    /

    返回文章
    返回