How can I highlight edge weight intensities in a weighted graph

Questions
1

I have a weighted graph, which I would like to plot using the AdjacencyGraph command or something similar. I can easily create the picture when the graph is unweighted using the AdjacencyGraph command. Is there an option for this command that will allow me to color the edges in a manner that conveys my graph’s varying weight values?

2

Hi Paul,

here I use Opacity to indicate the strength of the link:

windcm = # + Transpose[#] &@ RandomReal[{-0.5, 0.5}, {30, 30}];
CompleteGraph[30, VertexLabels -> "Name", 
 EdgeStyle ->  
  Flatten[Table[(i <-> j) -> 
     RGBColor[Map[1.0 - HeavisideTheta[-# - 0.15] &, windcm][[i, j]], 
      Map[HeavisideTheta[-Abs[#] + 0.15] &, windcm][[i, j]], 
      Map[1.0 - HeavisideTheta[-0.15 + #] &, windcm][[i, j]], 
      Map[0.75*Abs[#] &, windcm][[i, j]]], {i, 1, 30}, {j, 1, i}]]]

ScreenShot2015-11-11at01.42.53.jpg
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You see that I use RGBColor. Red indicates positive interaction, Blue negative interaction and the magnitude is represented by the different opacities. It is easy to adapt that to all sorts of colours, of course. This one would be for grayscale colouring:

CompleteGraph[30, VertexLabels -> "Name", 
EdgeStyle ->  Flatten[Table[(i <-> j) -> GrayLevel[1.5*Abs[windcm[[i, j]]]], {i, 1, 30}, {j, 1, i}]]]

Cheers,

Marco

3

The IGraph/M package makes such styling tasks fairly easy. Suppose you have the following adjacency matrix, containing weights:

wam = {{0, 10, 10, 0, 0, 0, 8, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 5, 18, 0, 
    0}, {5, 0, 0, 20, 0, 0, 0, 20, 0, 0}, {0, 0, 0, 0, 0, 0, 13, 0, 0,
     0}, {0, 0, 8, 0, 0, 11, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0}, {0, 0, 0, 19, 0, 0, 0, 17, 0, 0}, {0, 6, 0, 0, 0, 17, 0, 0, 0,
     0}, {0, 0, 0, 18, 19, 17, 0, 0, 0, 18}, {0, 0, 0, 0, 20, 0, 0, 0,
     0, 0}};

First we make a graph out of it:

g = IGWeightedAdjacencyGraph[wam, EdgeStyle -> Thick];

Then we style:

Legended[
 IGEdgeMap[ColorData["Rainbow"], EdgeStyle -> Rescale@*IGEdgeProp[EdgeWeight], g],
 BarLegend[{"Rainbow", MinMax@IGEdgeProp[EdgeWeight][g]}]
]

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