Is there a way to use UMAP on a weighted digraph?

I know If I have a weighted graph $G$(not a directed graph), I can define a metric on its vertices:
$$d(i,j) = text{weight of the minimum path between vertex i and j}$$
So I think It makes sense to use UMAP on distance matrix $A$ of graph $G$ that $A_{i,j} = d(i,j)$. Am I correct?

If $G$ is a directed weighted graph, How can I use UMAP?