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The phrase "a directed graph" is correct and usable in written English.
It can be used in contexts related to mathematics, computer science, or graph theory to describe a graph where the edges have a direction.
Example: "In our analysis, we will represent the relationships between the entities using a directed graph."
Alternatives: "a digraph" or "a directed network".
Exact(60)
If the edges have a direction, we speak of a directed graph, or a digraph.
In a directed graph, the edges have a direction from one node to the other.
Directed graphs : Let D= V,A) be a directed graph.
In fact, power grid can be abstracted as a directed graph according to power flow direction.
…what is known as a directed graph, or digraph.
For a directed graph, the results are similar.
So I'll remind you, a digraph is a directed graph.
Thus RDF models have the form of a directed graph.
The ancestry relationships found in provenance form a directed graph.
Johnson, D. B. Finding all the elementary circuits of a directed graph.
A walk through a directed graph that crosses each edge in the graph only once.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com