  We have studied the topology of the energy landscape of a spin-glass model
and the effect of frustration on it by looking at the connectivity and
disconnectivity graphs of the inherent structure. The connectivity network
shows the adjacency of energy minima whereas the disconnectivity network tells
us about the heights of the energy barriers. Both graphs are constructed by the
exact enumeration of a two-dimensional square lattice of a frustrated spin
glass with nearest-neighbor interactions up to the size of 27 spins. The
enumeration of the energy-landscape minima as well as the analytical mean-field
approximation show that these minima have a Gaussian distribution, and the
connectivity graph has a log-Weibull degree distribution of shape $\kappa=8.22$
and scale $\lambda=4.84$. To study the effect of frustration on these results,
we introduce an unfrustrated spin-glass model and demonstrate that the degree
distribution of its connectivity graph shows a power-law behavior with the
-3.46 exponent, which is similar to the behavior of proteins and Lennard-Jones
clusters in its power-law form.
