  In a network of spin 1/2 particles, controlled through an external
electro-magnetic field, the gyromagnetic ratio of each spin is a parameter that
characterizes the interaction of the spin with the external control field.
Multipartite networks are such that the spins are divided into subsets
according to their gyromagnetic ratio and spins in one set interact in the same
way with all spins in another set. Due to the presence of symmetries in this
type of systems, the underlying Hilbert state space splits into invariant
subspaces for the dynamics. Subspace controllability is verified if every
unitary evolution can be generated by the dynamics on these subspaces. We give
an exact characterization, in term of graph theoretic conditions, of subspace
controllability for multipartite quantum spin networks. This extends and
unifies previous results.
