D-separation

D-separation blocks paths through conditioned noncolliders and through unconditioned colliders without conditioned descendants.

On a path in a directed graph, an interior vertex is a collider when both adjacent path edges have arrowheads pointing into it. A path through a collider is blocked unless that collider or one of its descendants is conditioned upon.

An unshielded collider in a Directed acyclic graph is a triple $a\to b\leftarrow c$ with $a$ and $c$ nonadjacent. The absence of an edge between its outer vertices makes this orientation detectable from conditional independence information under faithfulness of a directed acyclic graph.

A set d-separates two vertex sets when it blocks every path between them.

Conditioned on its parents, a vertex is d-separated from all nondescendants other than those parents.

The global Markov property of a Directed acyclic graph says that d-separation of vertex sets $A$ and $B$ by $S$ implies conditional independence of the corresponding random vectors given the variables at $S$.