  We calculated the von Neumann entanglement entropy and the Schmidt number of
one dimentional (1D) cluster states and showed that these are useful measures
to estimate entanglement caused by delocalization of clusters. We analyze
system size dependence of these entanglement measures in the linear-chain
$n\alpha$ states given by Tohsaki-Horiuchi-Schuck-R\"opke wave functions for 1D
cluster gas states. We show that the Schmidt number is an almost equivalent
measures to the von Neumann entanglement entropy when the delocalization of
clusters occurs in the entire system but it shows different behaviors in a
partially delocalized state containing localized clusters and delocalized ones.
It means that the R\'enyi-2 entanglement entropy, which relates to the Schmidt
number, is found to be almost equivalent to the von Neumann entanglement
entropy for the full delocalized cluster system but it is less sensitive to the
partially delocalized cluster system than the von Neumann entanglement entropy.
We also propose a new entanglement measure which has a generalized form of the
Schmidt number. Sensitivity of these measures of entanglement to the
delocalization of clusters in low-density regions was discussed.
