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I mean I just made up the ratio but the 2 quantities are well-known things… a fractal would end up at like 0.7 or something for eg. Legible things would be 1
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Graph shortest path is very unlikely to honor the triangle inequality. Trying to apply spatial metaphors to graphs seems ill-fated, at best you can try to have edges represent orientational metaphors a la Lakoff and Johnson.
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I don’t understand what you’re talking about An illegible environment will have wiggly paths that will on average be longer than Euclidean shortest path, You’re not applying the triangle inequality on the graph. You’re applying it in the embedding space where it will work fine
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A lot of graphs aren't planar! If your graph *is* planar, then each vertex has a direct relationship to the nearby vertices on the plane, but if it isn't, then it may only have an indirect relationship to the neighbor, per whatever layout you've chosen.
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Fair enough, but I'm not sure that allows our spatial intuitions (which again, per Lakoff, are less spatial and more orientational) to be applied to non-trivial graphs.
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Sorry if I missed some context, but it didn't appear as if you were using legibility as a pejorative a la Scott, but something closer to Lynch's use of the term in Image of the City where it's aspirational.
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