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We generate a complete euclidean graph by taking N random points from a limited (1.0 x 1.0 square) 2D space, connecting them all together (complete graph) and giving the edges weights proportional (or equal) to the euclidean distance in space between the two incident points (euclidean graph).

If the random point generator in uniform, then if N is big enough it should be visible, that the points form a semi-regular grid of points.

I am to generate a Minimum Spanning Tree of such a graph (using Prim's algorithm).

The question is:
Should I expect any characteristic patterns of the tree?

Kindest regards,
Elmes

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The Math Overflow question at mathoverflow.net/questions/38824/… may be relevant here. –  Kevin Costello Mar 25 '12 at 8:59
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