  We analyze the expansion of the fuzzy sphere non-commutative product in
powers of the non-commutativity parameter. To analyze this expansion we develop
a graphical technique that uses spin networks. This technique is potentially
interesting in its own right as introducing spin networks of Penrose into
non-commutative geometry. Our analysis leads to a clarification of the link
between the fuzzy sphere non-commutative product and the usual deformation
quantization of the sphere in terms of the star-product.
