What are those weighed graphs called?

Question

Let $G = (V, E)$ be a directed graph, and define the weight function $f : V \sqcup E \to \mathbb{R}^+$ as follows:

1. sum of weights of vertices is 1,
2. if a vertex has edges coming out of it, their weights sum to 1, and
3. if a vertex has edges coming into it, their weights sum to 1.

I am curious if this weighted graph has a name in the literature.

Answer 1

For undirected graphs, constant weight of neighboring vertices has been called "weighted-regular", generalizing the concept of regular graph (when all the vertex weights are equal).

That definition is not used often enough to have become a standard term.