  The Green's function of the discrete Sch\"odinger operator on a finite graph
is considered. This setting reproduces Laplacian and signless Laplacian by
adjusting appropriate potentials. We show two ways of the expression for the
Green's function by using graph structures. The first way is based on the
factor of the graph by subtrees which have uni-self-loops; the second way is
based on that by odd unicycle graphs.
