 In all of these transitive closure algorithms , it is possible to distinguish pairs of vertices that are reachable by at least one path of length two or more from pairs that can only be connected by a length @-@ one path . The transitive reduction consists of the edges that form length @-@ one paths that are the only paths connecting their endpoints . Therefore , the transitive reduction can be constructed in the same asymptotic time bounds as the transitive closure . 
 In all of these transitive closure algorithms , it <a href='drop_aux' title='1'><mark>is</mark></a>possible to distinguish pairs of vertices <a href='null_relcl' title='2'><mark>that</mark></a>are reachable by at least one path of length two or more from pairs <a href='null_relcl' title='3'><mark>that</mark></a>can only be connected by a length @-@ one path . The transitive reduction <a href='uninflect' title='4'><mark>consists</mark></a> of the edges <a href='null_relcl' title='5'><mark>that</mark></a>form length @-@ one paths <a href='null_relcl' title='6'><mark>that</mark></a><a href='drop_aux' title='7'><mark>are</mark></a>the only paths connecting their endpoints . Therefore , the transitive reduction can be constructed in the same asymptotic time <a href='uninflect' title='8'><mark>bounds</mark></a> as the transitive closure . 
In all of dese transitive closure algorithms , it possible to distinguish pairs of vertices are reachable by at least one path of length two or more from pairs can only be connected by a length @-@ one path . The transitive reduction consist of the edges form length @-@ one paths the only paths connecting their endpoints . Therefore , the transitive reduction can b constructed in the same asymptotic time bound as the transitive closure .