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

• To: mathgroup at smc.vnet.net
• Subject: [mg87579] Re: [mg87545] Re: [mg87482] what does Method->"HighDimensionalEmbedding"
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 13 Apr 2008 03:34:15 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200804110547.BAA04959@smc.vnet.net> <200804121102.HAA00250@smc.vnet.net>
• Reply-to: murray at math.umass.edu

```I already tried all these methods, but choosing a method is not the
issue. There were two issues: first, how to make Mathematica create a
planar-embedded display of CompleteGraph (and more generally, any planar
graph); and second, what happened to one of the vertices and one of the
edges when I used Method -> "HighDimensionalEmbedding".

I now know an easy solution to the second issue -- see a separate post
as a follow-up to [mg87545]; the first one remains unresolved.

Syd Geraghty wrote:
> Murray,
>
> There is an example (below) from ref/GraphPlot in the Documentation
> under Options->Method,
>
> Apply a number of methods on the Petersen graph:
>
> << Combinatorica`
>
> Grid@Partition[
>    Table[GraphPlot[{1 -> 3, 1 -> 4, 2 -> 4, 2 -> 5, 3 -> 5, 6 -> 7, 7 -
>  > 8,
>       8 -> 9, 9 -> 10, 6 -> 10, 1 -> 6, 2 -> 7, 3 -> 8, 4 -> 9, 5 ->
> 10},
>      Method -> m, PlotLabel -> Style[m, Small], BaselinePosition -> Top,
>      ImageSize -> 150], {m, {"SpringElectricalEmbedding",
> "SpringEmbedding",
>       "HighDimensionalEmbedding", "CircularEmbedding",
> "RandomEmbedding",
>       "LinearEmbedding"}}], 3]
>
> The output diagrams the Method options for the Petersen graph.
>
> HTH
>
> Syd
>
>
> Syd Geraghty B.Sc, M.Sc.
>
> sydgeraghty at mac.com
>
> My System
>
> Mathematica 6.0.1 for Mac OS X x86 (64 - bit) (June 19, 2007)
> MacOS X V 10.5 .20
> MacBook Pro 2.33 Ghz Intel Core 2 Duo  2GB RAM
>
>
>
>
> On Apr 10, 2008, at 10:47 PM, Murray Eisenberg wrote:
> 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

```

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