  We study the spin squeezing property of weighted graph states, which can be
used to improve the sensitivity in interferometry. Decoherence reduces the spin
squeezing property but the result remains superior over other reference schemes
with GHZ-type maximally entangled states and product states. We study the time
evolution of spin squeezing of weighted graph states coupled to different
decoherence channels. Based on the analysis, the spin squeezing of the weighted
graph states is robust in the presence of decoherence and the decoherence limit
in the improvement of the interferometric sensitivity is still achievable.
