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Control Contribution Identifies Top Driver Nodes In Complex Networks

Author

Listed:
  • YAN ZHANG

    (Chair of Systems Design, ETH Zurich, Weinbergstrasse 58, 8092 Zurich, Switzerland)

  • ANTONIOS GARAS

    (Chair of Systems Design, ETH Zurich, Weinbergstrasse 58, 8092 Zurich, Switzerland)

  • FRANK SCHWEITZER

    (Chair of Systems Design, ETH Zurich, Weinbergstrasse 58, 8092 Zurich, Switzerland)

Abstract

We propose a new measure to quantify the impact of a node i in controlling a directed network. This measure, called “control contribution” 𝒞i, combines the probability for node i to appear in a set of driver nodes and the probability for other nodes to be controlled by i. To calculate 𝒞i, we propose an optimization method based on random samples of minimum sets of drivers. Using real-world and synthetic networks, we find very broad distributions of Ci. Ranking nodes according to their Ci values allows us to identify the top driver nodes that can control most of the network. We show that this ranking is superior to rankings based on other control-based measures. We find that control contribution indeed contains new information that cannot be traced back to degree, control capacity or control range of a node.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:acsxxx:v:22:y:2019:i:07n08:n:s0219525919500140
    DOI: 10.1142/S0219525919500140
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    References listed on IDEAS

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    1. Stefania Vitali & James B Glattfelder & Stefano Battiston, 2011. "The Network of Global Corporate Control," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-6, October.
    2. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    3. 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.
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    Cited by:

    1. 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.
    2. Yan Zhang & Frank Schweitzer, 2021. "Quantifying the importance of firms by means of reputation and network control," Papers 2101.05010, arXiv.org.
    3. Frank Schweitzer & Giona Casiraghi & Mario V. Tomasello & David Garcia, 2020. "Fragile, yet resilient: Adaptive decline in a collaboration network of firms," Papers 2011.13369, arXiv.org.
    4. Yu, Xiaoyao & Liang, Yongqing & Wang, Xiaomeng & Jia, Tao, 2021. "The network asymmetry caused by the degree correlation and its effect on the bimodality in control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).

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