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Graph partitions and the controllability of directed signed networks

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Abstract

This paper studies the controllability problem of signed networks which is presented by weighted and directed signed graphs. Graph partitions such as structural balance and almost equitable partitions (AEPs) are studied. We generalize the definition of AEPs to any graphs, directed or undirected, signed or unsigned, with or without edge weights. Based on AEP theory, a graph-theoretic necessary condition is proposed for the controllability of directed signed networks and an algorithm is given for the computation of the coarsest partition. Besides, the upper bound on the controllable subspace is derived when the system is uncontrollable.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61873136, 61374062, 61603288, 61673013), Natural Science Foundation of Shandong Province for Distinguished Young Scholars (Grant No. JQ201419), and Natural Science Foundation of Shandong Province (Grant No. ZR2016JL022).

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Authors and Affiliations

  1. Institute of Complexity Science, College of Automation and Electrical Engineering, Qingdao University, Qingdao, 266071, China

    Xianzhu Liu & Zhijian Ji

  2. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China

    Xianzhu Liu

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Ting Hou

Authors
  1. Xianzhu Liu
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  2. Zhijian Ji
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  3. Ting Hou
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Correspondence to Zhijian Ji.

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Liu, X., Ji, Z. & Hou, T. Graph partitions and the controllability of directed signed networks. Sci. China Inf. Sci. 62, 42202 (2019). https://doi.org/10.1007/s11432-018-9450-8

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  • DOI: https://doi.org/10.1007/s11432-018-9450-8

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