2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146136Recently, 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.4 pages, no figure. A presentation given at JGRG17 (Nagoya, Japan), to appear in the proceedingsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext