Characterization of Symmetry of Complex Networks
School of Sciences, Harbin Institute of Technology, Shenzhen 518055, China
Author to whom correspondence should be addressed.
Received: 27 April 2019 / Revised: 13 May 2019 / Accepted: 17 May 2019 / Published: 20 May 2019
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Recently, symmetry in complex network structures has attracted some research interest. One of the fascinating problems is to give measures of the extent to which the network is symmetric. In this paper, based on the natural action of the automorphism group
on the vertex set V
of a given network
, we propose three indexes for the characterization of the global symmetry of complex networks. Using these indexes, one can get a quantitative characterization of how symmetric a network is and can compare the symmetry property of different networks. Moreover, we compare these indexes to some existing ones in the literature and apply these indexes to real-world networks, concluding that real-world networks are far from vertex symmetric ones.
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MDPI and ACS Style
Chen, Y.; Zhao, Y.; Han, X. Characterization of Symmetry of Complex Networks. Symmetry 2019, 11, 692.
Chen Y, Zhao Y, Han X. Characterization of Symmetry of Complex Networks. Symmetry. 2019; 11(5):692.
Chen, Yangyang; Zhao, Yi; Han, Xinyu. 2019. "Characterization of Symmetry of Complex Networks." Symmetry 11, no. 5: 692.
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