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The phrase "a directed graph called a" is correct and usable in written English.
You can use it when introducing a specific type of directed graph in a mathematical or computer science context.
Example: "In this paper, we will explore a directed graph called a directed acyclic graph (DAG), which has important applications in scheduling and data processing."
Alternatives: "a directed graph referred to as a" or "a directed graph known as a".
Exact(2)
In their theory, a coupled cell system is a network of interacting dynamical systems whose coupling architecture is expressed by a directed graph called a coupled cell network.
Briefly, given an initial state, McMillan's algorithm gradually and implicitly records the states reachable from it by constructing a directed graph called a branching process.
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The signed directed graph, called a "model graph," is used for representing cause and effect relationships among process variables in a system, and a "Pattern" on the graph is introduced to represent a state of the system, which is specified by "0" for normal state, " + " and " − " for larger and smaller deviation from the normal state, respectively.
A directed graph (called digraph) is denoted by G= V,A), where A is the set of arcs (directed links).
For a given time points list and a set of temporal subnets obtained from Algorithm 1, by applying following Algorithm 2, we derive a directed graph, called active state transition diagram (ASTD), which is denoted by G = (N, E).
A node (edge) of a directed graph is called a cut-node (cut-edge) if its removal disconnects the graph.
A Click router is built by assembling several packet processing modules, called elements, forming a directed graph.
This information is called 'causal structure', and can be represented as a directed graph in which variables (measured or unmeasured) constitute nodes and causal relationships are represented as directed edges between nodes.
Directed graphs : Let D= V,A) be a directed graph.
We consider the natural adaptation of this game to directed graphs and show that monotone strategies in the game yield a measure, called dag-width, that can be seen to describe how close a directed graph is to a directed acyclic graph (dag).
A directed 1-forest – most commonly called a functional graph (see below), sometimes maximal directed pseudoforest – is a directed graph in which each vertex has outdegree exactly one.
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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