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transitive closure

transitive closure in Technology

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* z
I.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.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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