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wolfram-mathematicamathematica-8

How to Label Graph Edges with their weights

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?

Solution

  • 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