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We will introduce a class of graphs with coloured edges to encode root subsystems of the classical root systems, which in particular classify them up to the Weyl-group action, extending a previous construction for subsystems obtained from fission (which in turn are related to deformations of moduli spaces of meromorphic connections). We will further use these graphs to describe root-kernel intersections, as well as a natural quotient operation that corresponds to taking restrictions of rootarXiv:2206.03779v1 fatcat:2alld25rprh6jfzxu6fpddbc4q