  Recently, multi-graviton theory on a simple closed circuit graph
corresponding to the $S^1$ compactification of the Kaluza-Klein (KK) theory has
been considered. In the present paper, we extend this theory to that on a
general graph and study what modes of particles are included. Furthermore, we
generalize it in a possible non-linear theory based on the vierbein formalism
and study cosmological solutions.
