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$.$