D-separation

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In Bayesian networks, d-separation is a property of two nodes X and Y with respect to a set of nodes Z. X and Y are said to be d-separated by Z if no information can flow between them when Z is observed.

The d in d-separation stands for "directional". Informally, two variables X and Y are independent conditional on Z if knowledge about X gives you no extra information about Y once you have knowledge of Z. In other words, once you know Z, X adds nothing to what you know about Y.

Formally, a path p between two variables X and Y is blocked by a set of nodes Z if

p contains a chain i -> m -> j or a fork i <- m -> j such that m is in Z, or
p does not contain a collider i -> m <- j such that m or any of its descendants are in Z.