The transitive closure of a binary relation 
on a set 
is the minimal transitive
relation 
on 
that contains 
.
Thus 
for any elements 
and 
of 
provided that there exist 
, 
, ..., 
with 
, 
, and 
for all 
.
The transitive closure 
of a graph is a graph which contains
an edge 
whenever there is a directed path from 
to 
(Skiena 1990, p. 203). The transitive closure of a graph
can be computed using TransitiveClosure[g]
in the Wolfram Language package Combinatorica`
.
