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

**References**:**what does Method->"HighDimensionalEmbedding" actually do for GraphPlot?***From:*Murray Eisenberg <murray@math.umass.edu>

**Re: what does Method->"HighDimensionalEmbedding" actually do for GraphPlot?***From:*Syd Geraghty <sydgeraghty@mac.com>