  Using a graphical presentation of the spin $S$ one dimensional Valence Bond
Solid (VBS) state, based on the representation theory of the $SU(2)$
Lie-algebra of spins, we compute the spectrum of a mixed state reduced density
matrix. This mixed state of two blocks of spins $A$ and $B$ is obtained by
tracing out the spins outside $A$ and $B$, in the pure VBS state density
matrix. We find in particular that the negativity of the mixed state is
non-zero only for adjacent subsystems. The method introduced here can be
generalized to the computation of entanglement properties in Levin-Wen models,
that possess a similar algebraic structure to the VBS state in the groundstate.
