We call a hyperplane arrangement graphical if each hyperplane in it is
defined by an equation of the form $x_i-x_j=c$. Combining Carver's
variant of the Farkas' lemma with the Flow Decomposition Theorem we show
that the regions of any graphical arrangement may be bijectively labeled
with a set of weighted digraphs containing directed cycles of negative weight
only. Relatively bounded regions correspond to strongly connected digraphs. The
study of the resulting labelings allows us to add the omitted details in 
Stanley's  proof on the injectivity of the Pak-Stanley labeling of the
regions of the extended Shi arrangement, to generalize the ceiling
diagrams in the deleted Shi and Ish arrangements studied by Armstrong
and Rhoades and to introduce a new labeling of the regions in the
Fuss-Catalan arrangement. We also show how Athanasiadis-Linusson
labelings may be used to directly count regions in a class of
arrangements properly containing the extended Shi arrangement and the
Fuss-Catalan arrangement.