Is there an algorithm that shortens paths (and removes nodes) based on edge cost? I can't put it into words too well so I hope these images sum it up well enough:
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Are you looking for something out-of-the box or for algorithmic ideas on how to implement this yourself? I can help you with the latter.
What you want to do is called contraction of vertices which have exactly
2neighbours, i.e. that have degree2.For implementing this, do the following:
That is, if you have the following part of the graph:
u ---2--- v ---5--- wand apply the contraction, you end up withu ---7--- w.Just doing this iteratively until no vertex wit degree
2remains will transform the graph in the first picture into the graph in your second picture.The exact implementation details will, of course, depend on which data structure you use to represent your graph in Python (or any other language that is being used).