Let $G=(V,E,W)$ be an undirected weighted graph, where $V$ (resp. $E$) is the set of vertices (resp. edges) of $G$, and $W : E \to \mathbb{Z}_p$ is the edge weight assignment function. Note that weights in my definition are modular numbers. My impression (might be wrong)that works in graph theory (in particular, shortest paths results) assume that weights are from a characteristic zero field.
Question: are there existing results in graph theory where the edge weights are modular? In particular shortest path algorithms?