I faintly remember that we did `use` graph theory in our HS assignments, but haven't actually touched hypothesis or proofs, that I now associate with it.
I remember we wrote programs to higlight a graphs skelet, find shortest path, search for components, e.t.c.
Discussions on correctness and efficiency were informal.
Not US, but I learned graph theory in HS, so it is done in some countries (CS class though, not maths)