  Using a field-theoretical representation of the Tanaka-Edwards integral we
develop a method to systematically compute the number N_s of 1-spin-stable
states (local energy minima) of a glassy Ising system with nearest-neighbor
interactions and random Gaussian couplings on an arbitrary graph. In
particular, we use this method to determine N_s for K-regular random graphs and
d-dimensional regular lattices for d=2,3. The method works also for other
graphs. Excellent accuracy of the results allows us to observe that the number
of local energy minima depends mainly on local properties of the graph on which
the spin glass is defined.
