Consider a weighted directed graph G with positive weights on all edges.$$ Let d$($x$,$y$)$ denote the distance from x to y$.$

If $($u$,$ v$)$ is an edge in G and d$($s$,$u$)=$ d$($s$,$v$),$ then it is possible that the shortest s$-$v path ends with edge $($u$,$ v$).$