We develop a systematical way of constructing S-Ricci flat graphs which are not Abelian Cayley via graph bundle with explicit examples. For this purpose, we prove that, with some natural constrains, a non-trivial graph bundle can not be isomorphic (as graphs) to the product of the base graph and fiber graph. It stands in clear contrast to the continuous case.PDF: Graph bundles and Ricci-flatness.pdf