  We have studied the electronic structure of the Ni triangular lattice in
NiGa$_2$S$_4$ using photoemission spectroscopy and subsequent model
calculations. The cluster-model analysis of the Ni 2$p$ core-level spectrum
shows that the S 3$p$ to Ni 3$d$ charge-transfer energy is $\sim$ -1 eV and the
ground state is dominated by the $d^9L$ configuration ($L$ is a S 3$p$ hole).
Cell perturbation analysis for the NiS$_2$ triangular lattice indicates that
the strong S 3$p$ hole character of the ground state provides the enhanced
superexchange interaction between the third nearest neighbor sites.
