  Recently, a multigraviton theory on a simple closed circuit graph
corresponding to the discretization of $S^1$ 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 nonlinear theory based on
the vierbein formalism and study classical and quantum cosmological solutions
in the theory. We found that scale factors in a solution for this theory repeat
acceleration and deceleration.
