> I'm trying to draw a graph where the distance between vertices
> correspond to the edge weights. I know it is difficult to do, but I
> ask you if do you know any algorithm that minimizes the problems of
> this kind of plot. It would be so helpful if you could suggest it.

Multidimensional scaling is the algorithm you are looking for -- but it works 
only if you can assign a distance to every pair of vertices, not just the 
connected ones. See layout.mds in the R package. If you don't have a distance 
for every pair of vertices, you can still approximate the distance matrix by 
calculating the total weight of the shortest path between disconnected vertices.

Best,
T.


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