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This question is similar but not identical to a related question called: coloring-vertices-using-graphplot . I need to color the vertices of a graph according to a function, f that is defined on the nodes where it takes integer values. Here's a poor mans version of what I would like. Which I morphed from "coloring-vertices-using-graphplot".

f = {1, 1, 2, 2, 20}
aa = Flatten@Position[f, 1]
bb = Flatten@Position[f, 2]
cc = Flatten@Position[f, 20]
vs = Join@@MapThread[Thread[#1 -> #2] &, {{aa, bb, cc}, {Blue, Orange, Red}}]
mm = RandomChoice[{0, 1}, {5, 5}];
GraphPlot3D[mm, VertexRenderingFunction -> ({#2 /. vs, Sphere[#1, 0.05]} &)]

SOmething alone these lines would work since my "node function" f only takes on integer values, say from 1,2, ..., 20 but it seems that it would be better to use a color map.

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colorRules = Thread[DeleteDuplicates[f] -> {Blue, Red, Orange}];
mm = RandomChoice[{0, 1}, {5, 5}];

GraphPlot3D[mm, VertexRenderingFunction -> ({f[[#2]] /. colorRules, Sphere[#1, 0.05]} &)]

or

cF[1] = Blue;
cF[2] = Red;
cF[20] = Orange;
GraphPlot3D[mm, VertexRenderingFunction -> ({cF[f[[#2]]], Sphere[#1, 0.05]} &)]

gives

enter image description here

Alternatively, you can Rescale f and use it as input to ColorData functions:

f2 = {1, 1, 5, 5, 12}; 
GraphPlot3D[mm, VertexRenderingFunction -> ({ColorData["Rainbow"][Rescale[f2][[#2]]],
      Sphere[#1, 0.05]} &)]

enter image description here

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  • $\begingroup$ Very cool. I think this is exactly what I was after. Actually I want to use a fixed scale. I'll have a bunch of different versions of f2, one for each time point in a dynamical simulation. Ahh. I see. I can feed "Rescale" a fixed scale and I'm good to go. $\endgroup$ – JEP Dec 12 '14 at 17:55

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