Problem Detail: Given a weighted, undirected graph $G = (V,E)$, how can I compute the average weight of edges?
It seems an easy problem (divide the total weight to the number of edges!) but I couldn’t manage to find the sum of the edge weights since each edge can be counted several times while iterating through the vertices.
It seems an easy problem (divide the total weight to the number of edges!) but I couldn’t manage to find the sum of the edge weights since each edge can be counted several times while iterating through the vertices.
Asked By : cagirici
Answered By : Bartosz Przybylski
If $w(i,j)$ is the weight of edge $ij$ then: $avg = frac{1}{2|E|}sum_{ineq j}w(i,j)$. Why $2E$ ? Because when traversing vertices you will calculate both edges $ij$ and $ji$. Since it’s the same edge, you are adding its weight twice, so you need to remove this redundancy by dividing by 2.
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