  Disconnectivity graphs are used to visualize the minima and the lowest energy
barriers between the minima of complex systems. They give an easy and intuitive
understanding of the underlying energy landscape and, as such, are excellent
tools for understanding the complexity involved in finding low-lying or global
minima of such systems. We have developed a classification scheme that
categorizes highly-degenerate minima of spin glasses based on similarity and
accessibility of the individual states. This classification allows us to
condense the information pertained in different dales of the energy landscape
to a single representation using color to distinguish its type and a bar chart
to indicate the average size of the dales at their respective energy levels. We
use this classification to visualize disconnectivity graphs of small
representations of different tile-planted models of spin glasses. An analysis
of the results shows that different models have distinctly different features
in the total number of minima, the distribution of the minima with respect to
the ground state, the barrier height and in the occurrence of the different
types of minimum energy dales.
