transitive closure


transitive closure

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

x R y => x R* yx R y and y R* z => x R* z

I.e. elements are related by R* if they are related by Rdirectly or through some sequence of intermediate relatedelements.

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