  We introduce a class of graphs with coloured edges to encode subsystems of
the classical root systems, which in particular classify them up to
equivalence. We further use the graphs to describe root-kernel intersections,
as well as restrictions of root (sub)systems on such intersections,
generalising the regular part of a Cartan subalgebra. We also consider a slight
variation to encode the hyperplane arrangements only, showing there is a unique
noncrystallographic arrangement that arises. Finally, a variation of the main
definition leads to elementary classifications of closed and Levi root
subsystems.
