An uncertain variable, U, is said to depend on another variable, V, if knowing the outcome of V provides information about the outcome of U. Mathematically, U depends on V if {U | E} ≠ {U | V, E}, where E denotes the background state of information under which the dependence is asserted. In a relevance diagram, U's dependence on V can be explicitly represented at the level of structure by a conditioning arrow from V to U. However, a conditioning arrow from V to U is not sufficient to establish the dependence of U on V; U must also depend on V at the level of number (eg, an addition operation creates a new arrow without creating a numerical dependency). Furthermore, the absence of an arrow does not generally imply that U and V are independent; rather, it implies that U and V are conditionally independent given their direct predecessors.

See also: Mutual Independence, Pairwise Independence, Pedigree and Relevant.