  We point out that the total number of trails and the total number of paths of
given length, between two vertices of a simple undirected graph, are obtained
as expectation values of specifically engineered quantum mechanical
observables. Such observables are contextual with some background independent
theories of gravity and emergent geometry. Thus, we point out yet another
situation in which the mathematical formalism of a physical theory has some
computational aspects involving intractable problems.
