  It is well known that each nonnegative integral flow on a graph can be
decomposed into a sum of nonnegative graphic circuit flows, which cannot be
further decomposed into nonnegative integral sub-flows. This is equivalent to
saying that the indecomposable flows on graphs are those graphic circuit flows.
Turning from graphs to signed graphs, the indecomposable flows are much richer
than those of unsigned graphs. This paper gives a complete description of
indecomposable flows on signed graphs from the viewpoint of resolution of
singularities by means of double covering graphs.
