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How to layout a planar graph so that it doesn't have any intersecting edges?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg124990] How to layout a planar graph so that it doesn't have any intersecting edges?
*From*: Szabolcs HorvÃt <szhorvat at gmail.com>
*Date*: Thu, 16 Feb 2012 03:28:28 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
A planar graph is a graph that can be drawn in the plane so that no
two edges will intersect.
Combinatorica`PlanarQ will test if a graph is planar.
My question is: How can we draw a graph that is known to be planar
without intersecting edges in Mathematica? Is there a function /
method for this?
--------8<---------
I posted the same question here as well:
http://mathematica.stackexchange.com/q/1781/12
At the time when I'm writing this, there are no answers, but please
check that thread when you read this, in case any progress has been
made on the problem.
-------->8--------
For testing, here's some code which will randomly generate a number of
small planar graphs. All of these should be drawn without
intersecting edges by the method (they are not drawn like this by the
default layout algorithm)
<< ComputationalGeometry`
graphs = DeleteDuplicates[
Flatten@Table[
Graph@
Union[Sort /@
Join @@ (Thread /@
DelaunayTriangulation@RandomReal[1, {j, 2}])],
{25}, {j, 4, 12}
], IsomorphicGraphQ];
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