A signed graph is a finite simple graph 
together with a function 
assigning a sign
to each graph edge (Zaslavsky 1982). The sign of a
cycle graph is the product of its edge signs. Switching
at a graph vertex reverses the signs of all incident
edges and preserves every cycle sign. Reversing every
edge sign is a different operation.
The signed circular chromatic number measures the circumference needed for a circular coloring that respects the signs. It depends on the convention for positive and negative edges.
