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>