  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.
