  An efficient algorithm is developed to construct disconnectivity graphs by a
random walk over basins of attraction. This algorithm can detect a large number
of local minima, find energy barriers between them, and estimate local thermal
averages over each basin of attraction. It is applied to the SK spin glass
Hamiltonian where existing methods have difficulties even for a moderate number
of spins. Finite-size results are used to make predictions in the thermodynamic
limit that match theoretical approximations and recent findings on the free
energy landscapes of SK spin glasses.
