Back-door path

A back-door path in a causal graph is an indirect path with an arrow into the treatment variable.

Formally, given a graph with nodes including $X$ (treatment variable) and $Y$ (outcome variable), a direct path from $X$ to $Y$ is just a directed edge $X\to Y$. An indirect path from $X$ to $Y$ is some traversal of edges from $X$ to $Y$ that isn't a direct path. Importantly, the edges don't have to be pointed in the "right way", so $X\to Z\leftarrow W\to Y$ is an indirect path. A back-door path is an indirect path with an arrow into $X$.

Examples

$X\leftarrow Z\to Y$ is a back-door path from $X\to Y$

$X\to Z\leftarrow W\to Y$ is not a back-door path from $X\to Y$: it is an indirect path but there is no arrow into $X$