a ⇒ b b ⇒ e c ⇒ e c ⇒ d d ⇒ f e ⇒ f 
Corresponding directed graph:
a ⇒ b and b ⇒ c implies: a ⇒ c 
a < b and b < c implies: a < c 







Proof:

v_{1}, v_{2}, ..., v_{n} = an arbitrary numbering of the vertices G_{0} = G; // Initialize for ( k = 1; k <= n; k++ ) { G_{k} = G_{k1}; // Build next graph for ( i = 1; i <= n; i++ ) { for ( j = 1; j <= n; j++ ) { if ( edges (i,k) and (k,j) exists in G_{k} ) { add edge (i,j) to G_{k}; } } } } 