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Controllability of complex networks

Author

Listed:
  • Yang-Yu Liu

    (Computer Science and Biology, Northeastern University
    Center for Cancer Systems Biology, Dana-Farber Cancer Institute)

  • Jean-Jacques Slotine

    (Nonlinear Systems Laboratory, Massachusetts Institute of Technology
    Massachusetts Institute of Technology)

  • Albert-László Barabási

    (Computer Science and Biology, Northeastern University
    Center for Cancer Systems Biology, Dana-Farber Cancer Institute
    Brigham and Women’s Hospital, Harvard Medical School)

Abstract

The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.

Suggested Citation

  • Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    • Handle: RePEc:nat:nature:v:473:y:2011:i:7346:d:10.1038_nature10011
    DOI: 10.1038/nature10011
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