Local symmetries in complex networks

Details Local symmetries in complex networks Local symmetries in complex networks

2006-08-30

arxiv.org/abs/cond-mat/0608695v3

Journal of the Korean Physical Society 50, 300-303 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Presented at (and submitted to the proceedings of) Dynamics Days Asia Pacific 4

Scientific paper

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 the 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 networks. We discuss different precise definitions based on this idea and give examples how different symmetry coefficients can be applied to protein interaction networks.

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