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Characterization of Symmetry of Complex Networks

School of Sciences, Harbin Institute of Technology, Shenzhen 518055, China
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Symmetry 2019, 11(5), 692; https://doi.org/10.3390/sym11050692
Received: 27 April 2019 / Revised: 13 May 2019 / Accepted: 17 May 2019 / Published: 20 May 2019
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Abstract

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 Aut ( Γ ) of Γ on the vertex set V of a given network Γ = Γ ( V , E ) , 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. View Full-Text
Keywords: complex networks; symmetry index; group action; orbit decomposition; vertex symmetric networks complex networks; symmetry index; group action; orbit decomposition; vertex symmetric networks
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Chen, Y.; Zhao, Y.; Han, X. Characterization of Symmetry of Complex Networks. Symmetry 2019, 11, 692.

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