Ex) Article Title, Author, Keywords
J. Korean Phy. Soc. 2007; 50(9(1)): 300-303
Published online January 15, 2007 https://doi.org/10.3938/jkps.50.300
Copyright © The Korean Physical Society.
Symmetry---invariance to certain operators---is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent in many complex networks, we consider measures that are continuous rather than dichotomous. The main operator we suggest is permutations of paths of a certain length leading out from a vertex. If these paths are more similar (in some sense) than expected, the vertex is a local center of symmetry in the network. We discuss different precise definitions based on this idea and give examples how different symmetry coefficients can be applied to protein interaction networks.
Keywords: Complex networks, Symmetry
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