What are directed acyclic graphs?

Directed acyclic graphs, graphical model theory, causal diagrams, causal inference, observational studies, confounding, covariate adjustment, reporting practices Directed acyclic graphs (DAGs) are an increasingly popular approach for identifying confounding variables that require conditioning when estimating causal effects.

How do you know if a graph is acyclic?

A directed graph is acyclic if and only if it has a topological ordering. Adding the red edges to the blue directed acyclic graph produces another DAG, the transitive closure of the blue graph. For each red or blue edge u → v, v is reachable from u: there exists a blue path starting at u and ending at v.

What is the number of acyclic orientations?

The number of acyclic orientations is equal to |χ(−1)|, where χ is the chromatic polynomial of the given graph. The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow vertex.

Is a graph with a topological ordering acyclic?

A graph that has a topological ordering cannot have any cycles, because the edge into the earliest vertex of a cycle would have to be oriented the wrong way. Therefore, every graph with a topological ordering is acyclic. Conversely, every directed acyclic graph has at least one topological ordering.