I use graphs because we have a case where we need to schedule actions/programs but they themselves have "ingredients" or dependencies in a wild arrangement. So a topological sort of a graph is incredible to solve this and run those actions in order.
I don't think just plain graphs with topological sorting are considered advanced data structures? The're one of the first things you learn in a CS curriculum... whereas lots of the stuff in Demaine's course is stuff that pretty much doesn't even exist in most schools.
