KBG and GN-Theory

After solving some Graph Theory related problems KBG challenged Sameer to solve the following problem. There is an undirected graph consisting of $N$ vertices numbered from $1$ to $N$. For every pair of vertices $u$ and $v$ $(u \neq v)$ in the graph, there is a undirected weighted edge between $u$ and $v$ if and only if $u$ divides $v$, with weight $\frac{v}{u}$. Note that such a graph will not