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


*

*sum of weights of vertices is 1,

*if a vertex has edges coming out of it, their weights sum to 1, and

*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.

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.  
