The impact of graph symmetry on the number of driver nodes in complex networks |
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| Authors: | Hossein Parastvand Airlie Chapman Octavian Bass Stefan Lachowicz |
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| Institution: | 1. Smart Energy Systems Research Group, School of Engineering, Edith Cowan University, Australia;2. Department of Mechanical Engineering, School of Engineering, The University of Melbourne, Australia;1. Building 35B, Harbin Engineering University, Harbin, China;2. Ingkarni Wardli Building, North Terrace campus, The University of Adelaide, Adelaide, Australia;3. Building 61, Harbin Engineering University, Harbin, China;1. Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile;2. Departmento de Electricidad, Facultad de Ingeniería, Universidad Teconológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago, Chile;3. Facultad de Ingeniería y Arquitectura, Universidad Central de Chile, Toesca 1783, Santiago, Chile;4. Advanced Mining Technology Center, University of Chile, Av. Tupper 2007, Santiago, Chile;5. Department of Industrial Technologies, University of Santiago of Chile, Av. El Belloto 3735, Santiago, Chile;6. Facultad de Ingeniería y Tecnología, Universidad San Sebastián, Bellavista 7, Santiago 8420524, Chile;7. Escuela de Negocios y Tecnología, Universidad Gabriela Mistral, Av. Ricardo Lyon 1177, Providencia, Santiago, Chile;1. The School of Information and Control Engineering, Liaoning Shihua University, Fushun 113000, PR China;2. The Institute of Intelligence Science and Engineering, Shenzhen Polytechnic, Shenzhen 518055, PR China;3. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou Zhejiang 310027, PR China;1. Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China;2. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;3. Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, University of Science and Technology Beijing, Beijing 100083, China;4. Shunde Graduate School, University of Science and Technology Beijing, Foshan 528399, China |
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| Abstract: | This study investigates on a strong correlation between complex network (CN) controllability (characterized by the number of required driver nodes) and graph symmetry (described by automorphism groups) in undirected and unweighted networks. Based on the properties of permutation products of elementary automorphisms, novel necessary conditions for CN controllability are presented which are computationally more effective than previous method. In addition, a novel index of symmetry is proposed upon which a more meaningful understanding of symmetry impact on CN controllability can be comprehended. Based on this new index, a modification strategy is suggested aiming to satisfy CN controllability with a lower number of driver nodes. The study shows that the proposed modification approach can result in a minimal set of driver nodes with a reasonable computational complexity. Further, the critical components of complex networks, in terms of their impact on the number of required driver nodes, are identified. The results of the proposed methodologies have been verified for several synthetic and real test systems including small, medium, and large power networks. |
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