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Re: Re: what does Method->"HighDimensionalEmbedding" actually

• To: mathgroup at smc.vnet.net
• Subject: [mg87562] Re: [mg87532] Re: what does Method->"HighDimensionalEmbedding" actually
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 13 Apr 2008 03:31:06 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <ftmu54$4vq$1@smc.vnet.net> <200804121100.HAA00096@smc.vnet.net>
• Reply-to: murray at math.umass.edu

Yes, that reveals the hidden vertex and edge.  Thank you!  (I received a 
similar, private, response from another MathGroup subscriber.)

Unresolved, though, is a more fundamental functionality issue: how to 
get Mathematica directly to display a planar graph by means of a planar 
embedding (i.e., no edges intersect except at their common vertices) -- 
without manual intervention by the user.

There are well-known methods for determining whether a given graph is 
planar (including Kuratowski's Theorem), and I presume 
Combinatorica`PlanarQ already implements such a method.

But actually constructing a plane embedding of such a graph is another 
matter.  I had hoped that Mathematica could do this at least for 
relatively simple graphs.  It seems no.


Steve Luttrell wrote:
> The default display of the graph causes some of its edges to lie on top of 
> each other. If you click down to node 3 (3 clicks on the graphic of node 3) 
> you can then click-drag it sideways to reveal all of the edges.
> 
> Stephen Luttrell
> West Malvern, UK
> 
> "Murray Eisenberg" <murray at math.umass.edu> wrote in message 
> news:ftmu54$4vq$1 at smc.vnet.net...
>> What, exactly, is the "HighDimensionalEmbeedding" value for the
>> GraphPlot option Method?
>>
>> And why does the following produce a display that seems to be wrong: the
>> displayed graph has only 5 edges instead of the expected 6 for the
>> complete graph on 4 vertices?
>>
>>  GraphPlot[CompleteGraph[4], Method -> "HighDimensionalEmbedding",
>>     VertexLabeling -> True]
>> -- 
>> Murray Eisenberg                     murray at math.umass.edu
>> Mathematics & Statistics Dept.
>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>> University of Massachusetts                413 545-2859 (W)
>> 710 North Pleasant Street            fax   413 545-1801
>> Amherst, MA 01003-9305
>>
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • Re: what does Method->"HighDimensionalEmbedding" actually do for GraphPlot?
    • From: "Steve Luttrell" <steve@_removemefirst_luttrell.org.uk>