# Transitive closure

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.

< Previous Terms |
Terms Containing transitive closure |
Next Terms > |

transistor Transistor-Transistor Logic TRANSIT transition ad transitive |
context clash Reflexive transitive closure strongly connected component Subset-Equational Language transitive closure |
transit network Translation Look-aside Buffer Transmission Control Protocol transparent transparent audio coding |