How to Label Graph Edges with their weights

Asked 11/9, 2011 at 20:38 Answered 25/2, 2012 at 20:22

Solved wolfram-mathematica mathematica-8

Warning! I posted the question when Mathematica v 8.0 was the coolest kid. The bug has been solved as of version 9.0.1

The help for EdgeLabels states:

enter image description here

However:

CompleteGraph[4,
 EdgeWeight -> Range@6,
 VertexShapeFunction -> "Name",
 EdgeLabels -> "EdgeWeight"]

Results in:

enter image description here

So, no Edge Labels ... I guess it is a bug.

I used a nasty construct like:

adj = {{\[Infinity], 1, 1, 1, 1}, {1, \[Infinity], 2, 2, 2}, 
       {1, 2, \[Infinity], 2, 2}, {1, 2, 2, \[Infinity], 2}, 
       {1, 2, 2, 2, \[Infinity]}};

WeightedAdjacencyGraph[adj,
    VertexShapeFunction -> "Name", 
    EdgeLabels -> 
     MapThread[Rule,{EdgeList@#,AbsoluteOptions[#, EdgeWeight]/.{_ -> x_}-> x}], 
    GraphHighlight -> FindEdgeCover[#]]  
                                        &@ WeightedAdjacencyGraph[adj]

enter image description here

Better ideas?

Certainty answered 11/9, 2011 at 20:38 Comment(7)

Have you checked to see if it works using an adjacency matrix with the weights as the numbers in the matrix? I have a notebook (at home I think) that shows how to create weighted graphs with line thicknesses that are proportional to weights - a very popular presentation of data in my field. – Peria 12/9, 2011 at 1:23

Yes, it's at home. I can't help you for another nine hours, sorry :) – Peria 12/9, 2011 at 1:50

@Peria Thanks! I can wait, indeed! – Certainty 12/9, 2011 at 3:42

@belisarius & the four letter word: Graph unfortunately still has some serious problems, be cautious and verify verify verify ... Graph[] objects occasionally end up in a corrupted state causing some functions to either give a wrong result or crash. I've encountered problems with removing vertices and isomorphism testing in particular. – Cathrinecathryn 12/9, 2011 at 13:1

@Cathrinecathryn I seldom use the Graph functionality, and each time I've to navigate trough the complexities of choosing among the disjoint implementations in Mma. I really hope they will get it settled in v9! – Certainty 12/9, 2011 at 14:21

Interestingly, the EdgeLabels doc page on my 8.01/win7-64 version does NOT include the "EdgeWeight" value. – Preset 12/9, 2011 at 15:0

@belisarius Seems like the problem lies with EdgeWeights rather than EdgeLabels. (You may have already realized that. Your MapThread essentially generates weights on-the-fly.) – Hallucination 14/9, 2011 at 1:16

For a regular GraphPlot, you will need a slightly more complicated solution using EdgeRenderingFunction (documentation). Suppose you have an adjacency matrix where the elements are also the (directional) weights.

lilnums = {{0, 2., 1., 3., 0, 6.}, {0, 0, 1., 2., 0, 0}, {1., 8., 0, 2., 0, 
 2.}, {10., 13., 7., 0, 0, 10.}, {0, 0, 0, 0, 0, 0}, {4., 1., 1., 2.,
 2., 0}}

Here are some labels for the vertices, supposing you are drawing network diagrams for international inter-bank exposures (the original has a lot more countries!).

names = {"AT", "AU", "CA", "CH", "CL", "ES"}

The following does what you need. The tricks are the reference back to the adjacency matrix using the parts of #2 inside the part specification, to reference the correct elements of nums, and the Mean[#1] to locate the label at the midpoint of the edge. The slot #1 seems to hold the coordinates of the vertices.

GraphPlot[lilnums, DirectedEdges -> True, 
 VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .04], 
 Black, Text[names[[#2]], #1]} &), 
 EdgeRenderingFunction -> ({AbsoluteThickness[2], Red, 
 Arrowheads[0.02], Arrow[#1, 0.05], Black, 
 Text[Round@ Abs[(lilnums[[#2[[1]], #2[[2]]]] + 
   lilnums[[#2[[2]], #2[[1]]]])], Mean[#1], 
  Background -> Yellow]} &), VertexLabeling -> True, 
 ImageSize -> 600,  
  PlotLabel -> Style["Plot Label", Bold, 14, FontFamily -> "Arial"]]

enter image description here

Peria answered 12/9, 2011 at 10:25 Comment(4)

(Pedantic point, probably). Am I correct in thinking that for weights greater than 1 this plot contains multiple edge labels (and edges) each placed one-on-top of the other, and it that OK? (It possibly is). For printing purposes, say, will each be rendered in exactly the same place? (I have had similar problems with edge labelling in another field, hence the interest) – Stereoscopy 12/9, 2011 at 12:27

@TomD - I don't think so. The plot is the same if you instead have Sign[lilnums] as the first argument, and/or if the option MultiedgeStyle -> None is used. Timings are the same, too. – Peria 12/9, 2011 at 12:40

@Verbeia. Thanks for the clarification. I missed that point. – Stereoscopy 12/9, 2011 at 16:37

Check chat to see how I did the syntax highlighting – Peria 12/9, 2011 at 22:56

EdgeLabels -> "EdgeWeight" still doesn't work in 8.0.4 and no longer seems to be in the documentation. However, here is one solution that does work:

lilnums = {{0, 2., 1., 3., 0, 6.}, {0, 0, 1., 2., 0, 0}, {1., 8., 0, 2., 0, 2.},
  {10., 13., 7., 0, 0, 10.}, {0, 0, 0, 0, 0, 0}, {4., 1., 1., 2., 2., 0}}
names = {"AT", "AU", "CA", "CH", "CL", "ES"};
g = WeightedAdjacencyGraph[names, lilnums /. {0 -> \[Infinity]}, 
  VertexShapeFunction -> "Name" , ImagePadding -> 15];
SetProperty[g, EdgeLabels -> MapThread[#1 -> #2 &, 
  {EdgeList[g], PropertyValue[g, EdgeWeight]}]]

Holliman answered 25/2, 2012 at 20:22 Comment(1)

This works just fine. Using the same technique I modified the EdgeStyle so that the lines thickness is proportional to the edge weight. Just set this additional property:

EdgeStyle -> MapThread[#1 -> #2 &, {EdgeList[g], AbsoluteThickness[#] & /@ (1 + 3*Rescale[PropertyValue[g, EdgeWeight]])}]

– Boatwright 31/3, 2012 at 23:55

EdgeLabels works fine. EdgeWeights does not.

It may already be obvious from Belisarius' second example that the problem lies with EdgeWeights not EdgeLabels

Here's some additional evidence. EdgeLabels very gladly displays a variety of labels correctly. But when you ask mma to display "EdgeWeights", it incorrectly displays 1's, no matter what you've stored there.

CompleteGraph[4, VertexShapeFunction -> "Name",
 EdgeLabels -> {
   UndirectedEdge[1, 2] -> "hello", 
   UndirectedEdge[1, 4] -> "goodbye", UndirectedEdge[2, 3] -> 55, 
   UndirectedEdge[3, 4] -> \[Pi]/2, 
   UndirectedEdge[4, 2] -> 
   "\!\(\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(26\)]\)(-1\!\(\
   \*SuperscriptBox[\()\), \(i\)]\)\!\(\*SuperscriptBox[\(\[Theta]\), \
   \(n - i\)]\)", UndirectedEdge[1, 3] -> {a, b, c}}]

The bug is not unique to CompleteGraph. Graph and GridGraph have the same problem.

Hallucination answered 14/9, 2011 at 1:12 Comment(1)

In fact all Graph unctions share the bug. Thanks! – Certainty 14/9, 2011 at 1:45

The solution is easy. Upgrade to V 8.0.1 :)

At least that is what I have and it works there. (windows 7)

enter image description here

Btw, I do not know if the labels on the edges are correct, but at least it does put them on the figure, unlike your image).

Apatite answered 12/9, 2011 at 6:32 Comment(3)

I get the same output in 8.0.1 on a Mac OS X, but I don't think the weights should be 1 in every case, given the Range construct in his example. – Peria 12/9, 2011 at 10:28

@belisarius This is what I get too, but I agree with Verbeia that the numbers on the edges seem to be incorrect. – Preset 12/9, 2011 at 14:58

@Apatite Very strange indeed! EdgeWeights do not display properly for Graph either (in 8.0.1). Try:

Graph[{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 3,    3 \[UndirectedEdge] 1}, EdgeWeight -> {2, 3, 4},   EdgeLabels -> "EdgeWeight"]

– Hallucination 12/9, 2011 at 19:36

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