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Despite the integration of graphs and networks, multigraphs are not supported in Mathematica 8+.

In Mathematica 9+, GraphPlot misbehaves for multigraphs having labelled parallel edges:

GraphPlot[{{1 -> 2, "a"}, {1 -> 2, "b"}, {2 -> 1, "c"}}]
GraphPlot[{{1 -> 2, "a"}, {1 -> 2, "b"}, {2 -> 1, "c"}}, DirectedEdges -> True]

GraphPlot multidigraph misbehavior

GraphPlot multigraph misbehavior

EdgeRenderingFunction is passed the nonsense labels, so using it is out of the question.

Due to this bug, it appears there is no easy way for Mathematica 9+ to render a multigraph with labels.

Are there any workarounds, or should I look somewhere other than Mathematica?

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Related: mathematica.stackexchange.com/q/6282/5 –  rm -rf Apr 1 at 6:07
1  
This bug appears to obtain still in MMA 10; Try Graph[{Labeled[1 \[DirectedEdge] 2, "p"], Labeled[1 \[DirectedEdge] 2, "q"]}] for disappointing results. –  Reb.Cabin Sep 7 at 15:20

1 Answer 1

up vote 5 down vote accepted

Here is a manual EdgeRenderingFunction that you can start from if you supply your labels as lists.

erf = Module[{spacing = .2, 
     transform = 
      Last@FindGeometricTransform[#, {{0, 0}, {1, 0}}]}, {Text[#, 
        transform[{1/2, #2}]], 
       GeometricTransformation[
        Arrow[BSplineCurve[{{0, 0}, {1/3, #2}, {2/3, #2}, {1, 0}}, 
          SplineWeights -> {1, 10, 10, 1}]], transform]} & @@@ 
     Thread[{#3, 
       Table[spacing*a, {a, Length@#3}] - 
        spacing*(Length@#3 + 1)/2}]] &;

GraphPlot[{{1 -> 2, {"a"}}, {2 -> 3, {"b", "c", "d"}}, {3 -> 4, {"e", 
    "f"}}, {1 -> 5, {"g", "h", "i", "j"}}, {3 -> 6, {"k"}}}, 
 EdgeRenderingFunction -> erf]

enter image description here

To do the same with Graph instead of GraphPlot requires a bit more work because EdgeShapeFunctions for Graphs aren't given the labels. So you need to Fold across the edges of the Graph and replace the EdgeLabels with a custom EdgeShapeFunction containing the labels for each edge.

g = Graph[{Property[1 -> 2, EdgeLabels -> {"a"}], 
    Property[2 -> 3, EdgeLabels -> {"b", "c", "d"}], 
    Property[3 -> 4, EdgeLabels -> {"e", "f"}], 
    Property[1 -> 5, EdgeLabels -> {"g", "h", "i", "j"}], 
    Property[3 -> 6, EdgeLabels -> {"k"}]}];

es[labels_] := 
 Module[{spacing = .2, 
    transform = 
     Last@FindGeometricTransform[#, {{0, 0}, {1, 0}}]}, {Text[#, 
       transform[{1/2, #2}]], 
      GeometricTransformation[
       Arrow[BSplineCurve[{{0, 0}, {1/3, #2}, {2/3, #2}, {1, 0}}, 
         SplineWeights -> {1, 10, 10, 1}]], transform]} & @@@ 
    Thread[{labels, 
      Table[spacing*a, {a, Length@labels}] - 
       spacing*(Length@labels + 1)/2}]] &

g // Fold[
   RemoveProperty[{SetProperty[{#, #2}, 
       EdgeShapeFunction -> 
        es@PropertyValue[{#, #2}, EdgeLabels]], #2}, EdgeLabels] &, #,
    EdgeList@#] &

enter image description here

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