IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0044459.html
   My bibliography  Save this article

Control Centrality and Hierarchical Structure in Complex Networks

Author

Listed:
  • Yang-Yu Liu
  • Jean-Jacques Slotine
  • Albert-László Barabási

Abstract

We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network’s degree distribution. We show that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.

Suggested Citation

  • Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2012. "Control Centrality and Hierarchical Structure in Complex Networks," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-7, September.
    • Handle: RePEc:plo:pone00:0044459
    DOI: 10.1371/journal.pone.0044459
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0044459
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0044459&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0044459?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    4. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    5. Magnus Egerstedt, 2011. "Degrees of control," Nature, Nature, vol. 473(7346), pages 158-159, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hu, Ying & Yu, Yang & Mardani, Abbas, 2021. "Selection of carbon emissions control industries in China: An approach based on complex networks control perspective," Technological Forecasting and Social Change, Elsevier, vol. 172(C).
    2. Yin, Hongli & Zhang, Siying, 2016. "Minimum structural controllability problems of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 467-476.
    3. Xiaoqian Sun & Sebastian Wandelt & Xianbin Cao, 2017. "On Node Criticality in Air Transportation Networks," Networks and Spatial Economics, Springer, vol. 17(3), pages 737-761, September.
    4. Cai, Ning, 2017. "On quantitatively measuring controllability of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 282-292.
    5. Li, Sheng & Liu, Wenwen & Wu, Ruizi & Li, Junli, 2023. "An adaptive attack model to network controllability," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    6. Han, Fangyuan & Zio, Enrico, 2019. "A multi-perspective framework of analysis of critical infrastructures with respect to supply service, controllability and topology," International Journal of Critical Infrastructure Protection, Elsevier, vol. 24(C), pages 1-13.
    7. Nie, Sen & Wang, Xuwen & Wang, Binghong, 2015. "Effect of degree correlation on exact controllability of multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 98-102.
    8. repec:plo:pone00:0094998 is not listed on IDEAS
    9. Li, Jian & Dueñas-Osorio, Leonardo & Chen, Changkun & Shi, Congling, 2016. "Connectivity reliability and topological controllability of infrastructure networks: A comparative assessment," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 24-33.
    10. Ding, Jin & Lu, Yong-Zai & Chu, Jian, 2013. "Studies on controllability of directed networks with extremal optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6603-6615.
    11. Manuel Garcia-Herranz & Esteban Moro & Manuel Cebrian & Nicholas A Christakis & James H Fowler, 2014. "Using Friends as Sensors to Detect Global-Scale Contagious Outbreaks," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-7, April.
    12. Aming Li & Yang-Yu Liu, 2020. "Controlling Network Dynamics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(07n08), pages 1-19, February.
    13. Babak Ravandi & Forough S. Ansari & Fatma Mili, 2020. "Controllability Analysis Of Complex Networks Using Statistical Random Sampling," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(07n08), pages 1-15, January.
    14. Yang, Xu-Hua & Chen, Guang & Chen, Sheng-Yong, 2013. "The impact of connection density on scale-free distribution in random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2547-2554.
    15. Jiao, Bo & Nie, Yuan-ping & Shi, Jian-mai & Huang, Cheng-dong & Zhou, Ying & Du, Jing & Guo, Rong-hua & Tao, Ye-rong, 2016. "Scaling of weighted spectral distribution in deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 632-645.
    16. Li, Xin-Feng & Lu, Zhe-Ming, 2016. "Optimizing the controllability of arbitrary networks with genetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 422-433.
    17. Yan Zhang & Antonios Garas & Frank Schweitzer, 2019. "Control Contribution Identifies Top Driver Nodes In Complex Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(07n08), pages 1-15, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Hyeonchae & Jung, Woo-Sung, 2016. "Structural efficiency to manipulate public research institution networks," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 21-32.
    2. Jiang, Zhong-Yuan & Zeng, Yong & Liu, Zhi-Hong & Ma, Jian-Feng, 2019. "Identifying critical nodes’ group in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 121-132.
    3. Li, Xin-Feng & Lu, Zhe-Ming, 2016. "Optimizing the controllability of arbitrary networks with genetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 422-433.
    4. Yang Tang & Huijun Gao & Wei Zou & Jürgen Kurths, 2012. "Identifying Controlling Nodes in Neuronal Networks in Different Scales," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-13, July.
    5. Wouter Vermeer & Otto Koppius & Peter Vervest, 2018. "The Radiation-Transmission-Reception (RTR) model of propagation: Implications for the effectiveness of network interventions," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-21, December.
    6. Wu, Yali & Dong, Ang & Ren, Yuanguang & Jiang, Qiaoyong, 2023. "Identify influential nodes in complex networks: A k-orders entropy-based method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    7. Wang, Zhixiao & Zhao, Ya & Xi, Jingke & Du, Changjiang, 2016. "Fast ranking influential nodes in complex networks using a k-shell iteration factor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 171-181.
    8. Xu, Shuang & Wang, Pei, 2017. "Identifying important nodes by adaptive LeaderRank," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 654-664.
    9. Li, Sheng & Liu, Wenwen & Wu, Ruizi & Li, Junli, 2023. "An adaptive attack model to network controllability," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    10. Li, Meizhu & Zhang, Qi & Deng, Yong, 2018. "Evidential identification of influential nodes in network of networks," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 283-296.
    11. Sheikhahmadi, Amir & Nematbakhsh, Mohammad Ali & Zareie, Ahmad, 2017. "Identification of influential users by neighbors in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 517-534.
    12. Juanjuan Luo & Teng Fei & Meng Tian & Yifei Liu & Meng Bian, 2023. "Sensitivity metrics of complex network based on co-occurrence truth table: exemplified by a high-speed rail network," Journal of Geographical Systems, Springer, vol. 25(4), pages 519-538, October.
    13. Liu, Jian-Guo & Ren, Zhuo-Ming & Guo, Qiang, 2013. "Ranking the spreading influence in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4154-4159.
    14. Chen, Sai & Ding, Yueting & Zhang, Yanfang & Zhang, Ming & Nie, Rui, 2022. "Study on the robustness of China's oil import network," Energy, Elsevier, vol. 239(PB).
    15. Ghulam Muhiuddin & Sovan Samanta & Abdulrahman F. Aljohani & Abeer M. Alkhaibari, 2023. "A Study on Graph Centrality Measures of Different Diseases Due to DNA Sequencing," Mathematics, MDPI, vol. 11(14), pages 1-18, July.
    16. Ding, Jin & Lu, Yong-Zai & Chu, Jian, 2013. "Studies on controllability of directed networks with extremal optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6603-6615.
    17. Luka Naglić & Lovro Šubelj, 2019. "War pact model of shrinking networks," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-14, October.
    18. Babak Ravandi & Forough S. Ansari & Fatma Mili, 2020. "Controllability Analysis Of Complex Networks Using Statistical Random Sampling," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(07n08), pages 1-15, January.
    19. Abdelaty, Hatem & Mohamed, Moataz & Ezzeldin, Mohamed & El-Dakhakhni, Wael, 2022. "Temporal robustness assessment framework for city-scale bus transit networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    20. Jiang, Wenjun & Li, Peiyan & Fan, Tianlong & Li, Ting & Zhang, Chuan-fu & Zhang, Tao & Luo, Zong-fu, 2024. "Scalable rapid framework for evaluating network worst robustness with machine learning," Reliability Engineering and System Safety, Elsevier, vol. 252(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0044459. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.