Journal of the Korean Physical Society

pISSN 0374-4884 eISSN 1976-8524


Published online January 15, 2007

Copyright © The Korean Physical Society.

Local Symmetries in Complex Networks

Petter Holme

J. Korean Phys. Soc. 50(9(1)), 300 - 303 (2007)


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