from
The Free On-line Dictionary of Computing (8 July 2008)
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.