Transitive closure of a directed graph

Transitive closure of a directed graph --- транзитивное замыкание орграфа. Given a digraph [math]\displaystyle{ G = (V,A) }[/math], the transitive closure of [math]\displaystyle{ G }[/math] is the digraph [math]\displaystyle{ G^{+} = (V,A^{+}) }[/math] such that an arc [math]\displaystyle{ (x,y) }[/math] belongs to [math]\displaystyle{ A^{+} }[/math] iff there exists a path [math]\displaystyle{ P(x,y) }[/math] in [math]\displaystyle{ G }[/math].

Warshall's algorithm computes transitive closures in [math]\displaystyle{ {\mathcal O}(n^{3}) }[/math] time.