Problem solvers based on graphs are hard to get your head around at first, but then you get extremely elegant and powerful solutions to seemingly unsolvable problems.

The only gotchas are: 1) time to get your head around 2) algorithmic complexity of the resulting solution.

Graph theory is probably the most fulfilling math application in the computer science. In a way, graph-based algorithms do magic similar to AI but in a fully determined manner. If you think about it more broadly, a graph resembles a subset of a neural network but only with {0, 1} weights.