Consider two positively weighted graphs G $=($V$,$ E$,$ w$)$ and G$=($V$,$ E$,$ w$)$ with the

same vertices V and edges E such that, for any edge e in E$,$ we have w$($e$)=$ w$($e$)^2$

For any two vertices u$,$ v in V$,$ any shortest path between u and v in G$$is also a

shortest path in G$.$