English Computing Dictionary
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
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.