What do large random planar graphs look like?
Choose uniformly among, say, all unlabeled planar graphs with 1000 nodes, and assume the graph has been laid out with straight edges to maximize some notion of aesthetic elegance. How inelegant is a typical large random planar graph?
I suspect very inelegant: lots of long edges and very acute angles. Euclidean geometry is very specific and constraining among the many possible hyperbolic geometries.
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