Rings of quotients of incidence algebras and path algebras

We
compute the maximal right/left/symmetric rings of quotients of
finite dimensional incidence and graph algebras. We show that
these rings of quotients are Morita equivalent to incidence
algebras and path algebras respectively, with respect to simpler,
well determined partially ordered sets and finite quivers,
respectively. The geometric background of these algebras gives us
an intuitive idea of the construction of their maximal ring of
quotients.