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

*To*: mathgroup at smc.vnet.net*Subject*: [mg112138] Re: Weighted graphs with sum of weights determining vertex placement?*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Wed, 1 Sep 2010 06:29:03 -0400 (EDT)*References*: <i5idqu$jtl$1@smc.vnet.net>

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