Re: Axes in ShowGraph

*To*: mathgroup at smc.vnet.net*Subject*: [mg54305] Re: [mg54259] Axes in ShowGraph*From*: DrBob <drbob at bigfoot.com>*Date*: Wed, 16 Feb 2005 14:36:42 -0500 (EST)*References*: <200502150250.VAA27333@smc.vnet.net> <opsl80prh3iz9bcq@monster.ma.dl.cox.net> <001401c51385$62d37310$0200a8c0@NEWSONY>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

>> If you plot this Plot what? You could have posted the graph's InputForm, after all. Still, here's an attempt to do without it: Needs["DiscreteMath`Combinatorica`"] Needs["Graphics`Colors`"] {v, m} = {40, 66}; degrees = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4}; edges = {{2, 16}, {15, 1}, {16, 15}, {3, 20}, {17, 2}, {18, 17}, {19, 18}, { 20, 19}, {4, 27}, {21, 3}, {22, 21}, {23, 22}, {24, 23}, {25, 24}, {26, 25}, {27, 26}, {5, 32}, { 28, 4}, {29, 28}, {30, 29}, {31, 30}, {32, 31}, {6, 33}, { 33, 5}, {7, 20}, {21, 6}, {20, 21}, {8, 7}, {9, 35}, {19, 8}, { 22, 19}, {33, 22}, {34, 33}, {35, 34}, {10, 18}, {36, 9}, { 37, 36}, {30, 37}, { 25, 30}, { 38, 25}, {15, 38}, {18, 15}, {11, 16}, {17, 10}, {16, 17}, {12, 34}, \ {38, 11}, {24, 38}, {31, 24}, {39, 31}, {34, 39}, {13, 26}, {35, 12}, {40, 35}, {37, 40}, {29, 37}, {26, 29}, {14, 36}, {27, 13}, {28, 27}, {36, 28}, {1, 23}, {40, 14}, {39, 40}, {32, 39}, {23, 32}}; vertices = {{4.02, 11.02}, {3.71, 5.73}, {6.86, 13.27}, {-2.38, 8.83}, {1.69, 11.97}, {1.63, 14.08}, {7.4, 12.05}, { 7.54, 11.46}, {-3.85, 13.21}, {5.64, 6.52}, {2.66, 7.35}, {-0.42, 13.44}, {-0.79, 8.44}, {-1.83, 12.39}, { 3.831, 7.7952}, { 3.7865, 7.0362}, {4.2068, 6.9192}, {4.404, 7.3913}, {6.1905, \ 11.6673}, {6.4848, 12.372}, {5.6225, 12.6754}, {4.1706, 11.9777}, {2.7813, 11.3101}, {1.0725, 10.489}, {0.4406, 10.1853}, {-0.7015, 9.6366}, {-1.0597, 9.4644}, {-1.1438, 9.7837}, {-0.6631, 10.1546}, {-0.1153, 10.5772}, {0.707, 11.2116}, {1.2879, 11.6598}, {1.6789, 12.3605}, {-0.0049, 12.6192}, {-0.4754, 12.6915}, {-1.6347, 11.6483}, {-0.6062, 10.9233}, { 1.6612, 9.3248}, {0.3718, 11.8744}, {-0.5204, 12.0833}}; g = FromUnorderedPairs@edges Sort /@ edges == Edges@g Degrees@g == degrees Through[{V, M}@g] == {v, m} "\[SkeletonIndicator]Graph:<"66", "40", ""Undirec\ ted"">\[SkeletonIndicator]" True True True But the vertices aren't right: Vertices@g {{0.987688,0.156434},{0.951057,0.309017},{ 0.891007,0.45399},{0.809017,0.587785},{0.707107,0.707107},{ 0.587785,0.809017},{0.45399,0.891007},{0.309017,0.951057},{ 0.156434,0.987688},{ 0,1.},{-0.156434,0.987688},{-0.309017,0.951057},{-0.45399,0.891007},{-0.\ 587785,0.809017},{-0.707107,0.707107},{-0.809017,0.587785},{-0.891007,0.45399}\ ,{-0.951057,0.309017},{-0.987688, 0.156434},{-1.,0},{-0.987688,-0.156434},{-0.951057,-0.309017},{-0.891007,-\ 0.45399},{-0.809017,-0.587785},{-0.707107,-0.707107},{-0.587785,-0.809017},{-\ 0.45399,-0.891007},{-0.309017,-0.951057},{-0.156434,-0.987688},{0,-1.},{0.\ 156434,-0.987688},{0.309017,-0.951057},{0.45399,-0.891007},{0.587785,-0.\ 809017},{0.707107,-0.707107},{0.809017,-0.587785},{0.891007,-0.45399},{0.\ 951057,-0.309017},{0.987688,-0.156434},{1.,0}} So here's another try: g = FromUnorderedPairs@edges; g[[2]] = List /@ vertices; Sort /@ edges == Edges@g Degrees@g == degrees Through[{V, M}@g] == {v, m} Vertices@g == vertices True True True True This test still fails: edges==Edges@g False but it's an Undirected graph, so I'm satisfied (I guess), with the test Sort /@ edges == Edges@g. Finally, I can plot the graph with some HOPE that I'm seeing the same thing as you: sg=ShowGraph[g, ImageSize -> 600, Background -> Linen, VertexColor -> Cyan, VertexStyle -> Disk[0.035], VertexNumber -> True, VertexNumberPosition -> Center, TextStyle -> {FontSize -> 13, FontWeight -> Bold}, Axes -> True, PlotRange -> All]; As you say, the scale seems to bear no relationship to the vertex values. Comparison with this plot: ListPlot[vertices, ImageSize -> 500, Frame -> True] suggests it's just a scaling/location issue, however. Through[{Max, Min}@#] & /@ Transpose@Vertices@g s1 = Subtract @@@ % Divide @@ s1 {{7.54,-3.85},{14.08,5.73}} {11.39,8.35} 1.36407 Through[{Max, Min}@#] & /@ Transpose@Cases[sg, Point[x_] -> x, Infinity] s2 = Subtract @@@ % Divide @@ s2 {{0.635248,0.},{1.,0.5343}} {0.635248,0.4657} 1.36407 s1/s2 {17.93,17.93} Scaling and translation were applied to (1) maintain aspect ratios, (2) make the minimum x value 0, (3) make the maximum y value 1, and (4) put all x and y values in Interval[{0,1}]. I don't think those rules completely determine the transformation, but that seems to be the general idea. Anyway, leave out Axes->True, and you'll never notice. The numerical values don't matter anyway, do they? Bobby On Tue, 15 Feb 2005 09:40:05 -0800, Steve Gray <stevebg at adelphia.net> wrote: > Bobby, > > Here, I think, is all the info you need. If you plot this you will see a > graph which is really a self-crossing polygon with 14 vertices (degree 2 > nodes) and 26 edge intersections (degree 4 n odes). The simplest eulerian > cycle in this case is just a complete circuit from one vertex to the next, > through the intervening intersections, back to the first vertex. I need the > eulerian cycle not for this graph but for a version of it with certain > vertices and edges removed. This 14-gon is just an example, but unless it > works, I can't proceed with the real problem(s). > > Thanks very much for your attention. > > Steve > > In[183]:= > comgraph > V[comgraph] > M[comgraph] > ver = Vertices[comgraph] > edg = Edges[comgraph] > Degrees[comgraph] > Out[183]= > \[SkeletonIndicator]Graph:<\[InvisibleSpace]66\[InvisibleSpace], \ > \[InvisibleSpace]40\[InvisibleSpace], \[InvisibleSpace]Undirected\ > \[InvisibleSpace]>\[SkeletonIndicator] > Out[184]= > 40 > Out[185]= > 66 > Out[186]= > {{4.02, 11.02}, {3.71, 5.73}, {6.86, 13.27}, {-2.38, 8.83}, {1.69, > 11.97}, {1.63, 14.08}, {7.4, 12.05}, {7.54, 11.46}, {-3.85, 13.21}, {5.64, > 6.52}, {2.66, 7.35}, {-0.42, 13.44}, {-0.79, 8.44}, {-1.83, > 12.39}, {3.831, 7.7952}, {3.7865, 7.0362}, {4.2068, 6.9192}, {4.404, > 7.3913}, {6.1905, 11.6673}, {6.4848, 12.372}, {5.6225, 12.6754}, {4.1706, > 11.9777}, {2.7813, 11.3101}, {1.0725, 10.489}, {0.4406, > 10.1853}, {-0.7015, 9.6366}, {-1.0597, 9.4644}, {-1.1438, > 9.7837}, {-0.6631, 10.1546}, {-0.1153, 10.5772}, {0.707, > 11.2116}, {1.2879, 11.6598}, {1.6789, 12.3605}, {-0.0049, > 12.6192}, {-0.4754, 12.6915}, {-1.6347, 11.6483}, {-0.6062, > 10.9233}, {1.6612, 9.3248}, {0.3718, 11.8744}, {-0.5204, 12.0833}} > Out[187]= > {{2, 16}, {15, 1}, {16, 15}, {3, 20}, {17, 2}, {18, 17}, {19, 18}, {20, > 19}, {4, 27}, {21, 3}, {22, 21}, {23, 22}, {24, 23}, {25, 24}, {26, > 25}, {27, 26}, {5, 32}, {28, 4}, {29, 28}, {30, 29}, {31, 30}, {32, > 31}, {6, 33}, {33, 5}, {7, 20}, {21, 6}, {20, 21}, {8, 7}, {9, 35}, {19, > 8}, {22, 19}, {33, 22}, {34, 33}, {35, 34}, {10, 18}, {36, 9}, {37, > 36}, {30, 37}, {25, 30}, {38, 25}, {15, 38}, {18, 15}, {11, 16}, {17, > 10}, {16, 17}, {12, 34}, {38, 11}, {24, 38}, {31, 24}, {39, 31}, {34, > 39}, {13, 26}, {35, 12}, {40, 35}, {37, 40}, {29, 37}, {26, 29}, {14, > 36}, {27, 13}, {28, 27}, {36, 28}, {1, 23}, {40, 14}, {39, 40}, {32, > 39}, {23, 32}} > Out[188]= > {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, > \ > 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4} > > ----- Original Message ----- > > From: "DrBob" <drbob at bigfoot.com> To: mathgroup at smc.vnet.net > To: "Steve Gray" <stevebg at adelphia.net>; <mathgroup at smc.vnet.net> > Sent: Tuesday, February 15, 2005 9:11 AM > Subject: [mg54305] Re: [mg54259] Axes in ShowGraph > > >> If we had a value for "comgraph", we might see what you're talking about. >> >> Bobby >> >> On Mon, 14 Feb 2005 21:50:55 -0500 (EST), Steve Gray > <stevebg at adelphia.net> wrote: >> >> > I have a graph with 40 vertices, displayed with this function: >> > >> > ShowGraph [ comgraph, >> > ImageSize -> 600, >> > Background -> RGBColor[.9, 1., .9], >> > VertexColor -> RGBColor[.5, .9, .9], >> > VertexStyle -> Disk[0.03], >> > VertexNumber -> True, >> > VertexNumberPosition -> Center, >> > TextStyle -> {FontSize -> 13, FontWeight -> Bold}, >> > Axes -> True, >> > PlotRange -> All >> > ]; >> > >> > Everything looks correct except the values displayed on the axes bear no > relation to the >> > values of the vertices given by Vertices[comgraph]. > (PlotRange->Automatic does the same thing.) >> > The vertices have the values shown below, while the displayed axes run > from about 0 to 0.64 on >> > X and .53 to 1.0 on Y. I need the actual vertex coordinates displayed as > they are given here: >> > >> > In[50]:= >> > Vertices[comgraph] >> > >> > Out[50]= >> > {{4.02,11.02},{3.71,5.73},{6.86,13.27},{-2.38,8.83},{1.69,11.97},{1.63, >> > 14.08},{7.4,12.05},{7.54,11.46},{-3.85,13.21},{5.64,6.52},{2.66, >> > > 7.35},{-0.42,13.44},{-0.79,8.44},{-1.83,12.39},{3.831,7.7952},{3.7865, >> > 7.0362},{4.2068,6.9192},{4.404,7.3913},{6.1905,11.6673},{6.4848, >> > 12.372},{5.6225,12.6754},{4.1706,11.9777},{2.7813,11.3101},{1.0725, >> > 10.489},{0.4406,10.1853},{-0.7015,9.6366},{-1.0597,9.4644},{-1.1438, >> > 9.7837},{-0.6631,10.1546},{-0.1153,10.5772},{0.707,11.2116},{1.2879, >> > > 11.6598},{1.6789,12.3605},{-0.0049,12.6192},{-0.4754,12.6915},{-1.6347, >> > > 11.6483},{-0.6062,10.9233},{1.6612,9.3248},{0.3718,11.8744},{-0.5204, >> > 12.0833}} >> > >> > Users of the Graph functions are probably in the minority, but can > anyone explain this? >> > >> > Steve Gray >> > >> > >> > >> > >> >> >> >> -- >> DrBob at bigfoot.com >> www.eclecticdreams.net >> > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Axes in ShowGraph***From:*Steve Gray <stevebg@adelphia.net>

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