Symmetry-based structure entropy of complex networks |
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Authors: | Yang-Hua Xiao Wen-Tao Wu Momiao Xiong Wei Wang |
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Affiliation: | a Department of Computing and Information Technology, Fudan University, ShangHai 200433, PR China b Business school, University of Shanghai for Science and Technology, Shanghai 200433, PR China c Theoretical Systems Biology Lab, School of Life Science, Fudan University, Shanghai 200093, PR China d Human Genetics Center, University of Texas Health Science Center at Houston, Houston TX 77225, USA |
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Abstract: | Precisely quantifying the heterogeneity or disorder of network systems is important and desired in studies of behaviors and functions of network systems. Although various degree-based entropies have been available to measure the heterogeneity of real networks, heterogeneity implicated in the structures of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropies. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are more heterogeneous in the view of automorphism partition than what have been depicted under the measurement of degree-based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks. |
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Keywords: | Structure entropy Symmetry Complex network |
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