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Control Centrality and Hierarchical Structure in Complex Networks

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  • 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
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    References listed on IDEAS

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    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
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    3. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    4. Magnus Egerstedt, 2011. "Degrees of control," Nature, Nature, vol. 473(7346), pages 158-159, May.
    5. 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.
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    Citations

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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. Cai, Ning, 2017. "On quantitatively measuring controllability of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 282-292.
    13. 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.
    14. 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.
    15. 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.
    16. 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.

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