The transitive closure R* of a relation R is defined by

x R y => x R* y x R y and y R* z => x R* zI.e. elements are related by R* if they are related by R directly or through some sequence of intermediate related elements.

E.g. in graph theory, if R is the relation on nodes "has an edge leading to" then the transitive closure of R is the relation "has a path of zero or more edges to". See also Reflexive transitive closure.

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**Nearby terms:**
TRANSIT « transition ad « transitive « **transitive closure** » transit network » Translation Look-aside Buffer » Transmission Control Protocol

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Copyright Denis Howe 1985