TIME FOR SOME GRAPH THEORY
folks is there a measure that's like graph density but constant(ish) for number of nodes?
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Degree distribution statistics? I've seen average degree used a lot for modeling intrinsic density in a size-independent way
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mm I guess for a tree the degree distribution would be very close to constant (a polygon would be exactly constant)
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You want to generalize that? Ratio of (number of actual edges) to (number of edges in minimum spanning tree)
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I am interested in graphs that are slightly denser than a tree but the same relative density to the number of nodes no matter how many
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so yeah that sounds close; also what would be interesting is the densest graph for number of nodes which is nevertheless still planar.
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Look into graph laplacians for some food potentially relevant machinery here

