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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
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