Circular flow on signed graphs

The circular flow number @F"c(G,@s) of a signed graph (G,@s) is the minimum r for which an orientation of (G,@s) admits a circular r-flow. We prove that the circular flow number of a signed graph (G,@s) is equal to the minimum imbalance ratio of an orientation of (G,@s). We then use this result to prove that if G is 4-edge-connected and (G,@s) has a nowhere zero flow, then @F"c(G,@s) (as well as @F(G,@s)) is at most 4. If G is 6-edge-connected and (G,@s) has a nowhere zero flow, then @F"c(G,@s) is strictly less than 4.