Re: Weighted graphs with sum of weights determining vertex placement?

*To*: mathgroup at smc.vnet.net*Subject*: [mg112140] Re: Weighted graphs with sum of weights determining vertex placement?*From*: Luci Ellis <luci at verbeia.com>*Date*: Thu, 2 Sep 2010 02:29:45 -0400 (EDT)*References*: <i5idqu$jtl$1@smc.vnet.net> <i5l9t5$7ki$1@smc.vnet.net>

Thanks Sjoerd, This was a really good suggestion. It turns out, though, that some of the lesser-known options to the function do the trick, namely the "RepulsiveForcePower" and "StepLength" suboptions to Method -> "SpringElectricalEmbedding" . Using a construction like the below gave good results for q = -0.6 and r = 1.4. NB you get both arrows, on top of one another, using DirectedEdges -> True, MultiedgeStyle -> False. Manipulate[ GraphPlot[rawnums, DirectedEdges -> True, MultiedgeStyle -> False, VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .04], Black, Text[names[[#2]], #1]} &), EdgeRenderingFunction -> (With[{relexp = (rawnums[[#2[[1]], #2[[ 2]]]])/100}, {AbsoluteThickness[relexp*20.], RGBColor[relexp*0.8, relexp*0.8, relexp*0.8], Arrowheads[0.06 relexp + 0.008], Arrow[#1, 0.05]}] &), VertexLabeling -> True, ImageSize -> 500, PlotLabel -> Style["Plot Heading", Bold, 14, FontFamily -> "Arial"], ImagePadding -> 0, PlotRange -> All, PlotRangePadding -> 0.02, Method -> {"SpringElectricalEmbedding", "RepulsiveForcePower" -> q, "StepLength" -> r}], {q, -4, -0.01}, {r, 1., 5.}] This function might come in handy for some purposes. I used it to verify that you get the same result for adjacency matrices as for lists of rules, and regardless of whether you actually show all the multiedges. AdjacencyMatrixToRules[mat_?MatrixQ] /; Equal @@ Dimensions[mat] := With[{n = Length[mat]}, Flatten@(Join @@ Table[Table[i -> j, {mat[[i, j]]}], {i, n}, {j, n}]) ] Hope that helps. Best regards, Luci On 2010-09-01 20:28:53 +1000, Sjoerd C. de Vries said: > With the total weigths in the list sums (sums = Total /@ rawnums) I > suppose various constructions like > > VertexCoordinateRules -> ((Max[sums] - sums) ({Cos[#], Sin[#]} & /@ > Table[i, {i, 0, 2 \[Pi] - 2 \[Pi]/8, 2 \[Pi]/8}])) > > or > > VertexCoordinateRules -> ((8 - > Ordering[Ordering[sums]]) ({Cos[#], Sin[#]} & /@ > Table[i, {i, 0, 2 \[Pi] - 2 \[Pi]/8, 2 \[Pi]/8}])) > > may meet your needs. > > Cheers -- Sjoerd > > On Aug 31, 10:17 am, Luci Ellis <l... at verbeia.com> wrote: >> Dear all, >> Suppose I have a weighted adjacency matrix like this: >> >> rawnums={{0, 43, 25, 70, 92, 75, 83, 69}, {0, 0, 0, 0, 0, 0, 0, 2}, {6, >> 28, 0, 1, 0, >> 3, 0, 3}, {26, 1, 2, 0, 4, 1, 7, 14}, {0, 2, 1, 0, 0, 1, 0, 0}, {7, 1= > 8, 60, >> 0, 1, 0, 2, 10}, {49, 2, 2, 6, 3, 7, 0, 1}, {12, 5, 10, 23, 0, 13, 7,= > 0}} >> >> Some vertex labels: >> names = ToString /@ Range[8] >> >> And some code to create a graph with edge thickness based on the >> weights, like this: >> >> GraphPlot[Sign[rawnums], DirectedEdges -> True, MultiedgeStyle -> True, >> VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .04], Bla= > ck, >> Text[names[[#2]], #1]} &), >> EdgeRenderingFunction -> (With[{relexp = (rawnums[[#2[[1]], #2[[2]]]= > ])/ >> 100}, {AbsoluteThickness[relexp*20.], >> RGBColor[relexp*0.8, relexp*0.8, relexp*0.8], >> Arrowheads[0.06 relexp + 0.008], Arrow[#1, 0.05]}] &), >> VertexLabeling -> True, ImageSize -> 500, >> ImagePadding -> 0, PlotRange -> All, PlotRangePadding -> 0.02] >> >> How do I get the vertices with the highest total weights (in this case >> the sum of each row, since all the columns sum to 100), to sit in the >> centre of the graph, with the less connected / lower-weighted vertices >> at the periphery? I have tried all the alternatives in the Method >> option. VertexCoordinateRules should do the trick, but I have no idea >> how to specify those rules according to the weights. >> Any suggestions? I am not a graph theorist so this is new to me. >> >> Best regards, >> Luci