On the basis of density-functional theory (DFT) calculations, a theoretical analysis of the exchange interactions in Ni9L2(O2CMe)(8){(2-py)(2)CO2}(4), was performed, where L is a bridging ligand, OH- (1) or N-3(-) (2). Each magnetic interaction between the Ni spin centers is analyzed for 1 and 2 in terms of exchange integrals (J values), orbital overlap integrals (T values) and natural orbitals. It was found that a J(3) interaction, which is a magnetic interaction via the bridging ligand orbitals, mainly controls the whole magnetic properties, and the dominant interaction is a a-type orbital interaction between Ni d(z)(2) orbitals. Further investigations on the magnetostructural correlations are performed on the J(3) interactions using simplest Ni-L-Ni models. These models reproduced the magnetic interactions qualitatively well not only for the Ni-9 complexes but also for other inorganic complexes. Strong correlations have been found between the magnetic orbital overlaps (T values) and the Ni-L-Ni angle. These results revealed that the difference of the magnetic properties between OH- and N-3(-) is caused by the orbital overlap integral (T values) of the a-type J3 interaction pathway. The magnetic interactions are also discussed from a Hubbard model by evaluating the transfer integral (t) and on-site Coulomb integrals (U), in relation to the Heisenberg picture.