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Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks

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  • Noah J Cowan
  • Erick J Chastain
  • Daril A Vilhena
  • James S Freudenberg
  • Carl T Bergstrom

Abstract

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167–173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set, is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.

Suggested Citation

  • Noah J Cowan & Erick J Chastain & Daril A Vilhena & James S Freudenberg & Carl T Bergstrom, 2012. "Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-5, June.
    • Handle: RePEc:plo:pone00:0038398
    DOI: 10.1371/journal.pone.0038398
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    References listed on IDEAS

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    6. 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.
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    11. Theodore Mariolis & Despoina Kesperi, 2022. "Demand multipliers and technical performance of a Southern Eurozone economy in hard times: Kalman–Leontief–Sraffa evidence from the Greek economy, 2010–2014," Evolutionary and Institutional Economics Review, Springer, vol. 19(1), pages 47-75, April.
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    13. Chen, Shi-Ming & Xu, Yun-Fei & Nie, Sen, 2017. "Robustness of network controllability in cascading failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 536-539.

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