### Abstract

Original language | English |
---|---|

Article number | 28037 |

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Scientific Reports |

Volume | 6 |

DOIs | |

Publication status | Published - 21 Jun 2016 |

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### Cite this

*Scientific Reports*,

*6*, 1-12. [28037]. https://doi.org/10.1038/srep28037

**Control efficacy of complex networks.** / Gao, Xin-Dong; Wang, Wen-Xu; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Scientific Reports*, vol. 6, 28037, pp. 1-12. https://doi.org/10.1038/srep28037

}

TY - JOUR

T1 - Control efficacy of complex networks

AU - Gao, Xin-Dong

AU - Wang, Wen-Xu

AU - Lai, Ying-Cheng

N1 - Acknowledgements W.-X.W. was supported by CNNSF under Grant No. 61573064, and No. 61074116 the Fundamental Research Funds for the Central Universities and Beijing Nova Programme, China. Y.-C.L. was supported by ARO under Grant W911NF-14-1-0504.

PY - 2016/6/21

Y1 - 2016/6/21

N2 - Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver node. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.

AB - Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver node. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.

U2 - 10.1038/srep28037

DO - 10.1038/srep28037

M3 - Article

VL - 6

SP - 1

EP - 12

JO - Scientific Reports

JF - Scientific Reports

SN - 2045-2322

M1 - 28037

ER -