  To a digraph with a choice of certain integral basis, we construct a CW
complex, whose integral singular cohomology is canonically isomorphic to the
path cohomology of the digraph as introduced in \cite{GLMY}. The homotopy type
of the CW complex turns out to be independent of the choice of basis. After a
very brief discussion of functoriality, this construction immediately implies
some of the expected but perhaps combinatorially subtle properties of the
digraph cohomology and homotopy proved very recently \cite{GLMY2}. Furthermore,
one gets a very simple expected formula for the cup product of forms on the
digraph. On the other hand, we present an approach of using sheaf theory to
reformulate (di)graph cohomologies. The investigation of the path cohomology
from this framework, leads to a subtle version of Poincare lemma for digraphs,
which follows from the construction of the CW complex.
