Given a Undirected Weighted Planar Graph with $N$ nodes and $N-1$ edges each having different weight $w$. Between two nodes there is exactly one path that goes through the edges and nodes such that no node appears in the path more than once.
Given some nodes $A$1, $A$2$, ...,A$ K. $2$ nodes are taken at random from these nodes.
How to calculate the distance between those two randomly chosen nodes ?( The answer will be in a form of rational numbers)
By the way, I tried taking all pairs of points in the list $A$1, $A$2$, ...,A$ K and added sum of the distances between them i.e $(k*(k-1))/2$ pairs and divided it by K i.e. total number of points in the list. But this gives wrong answer. It is giving more in numerator.