Graph with VertexLabels and formatting function not working

[Tom_Verhoeff]

In Mathematica 9, the built-in graph facility allows you to control the rendering of vertex labels through the option VertexLabels. E.g.

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VertexLabels -> Placed["Name",Tooltip]

shows the vertex itself as vertex label in a tooltip when the mouse is hovered over the vertex.

According to the documentation you can also apply your own formatting function f to the label, by providing f as a third argument to Placed. However, in the examples with VertexLabels, the vertex labels in that case are forced to some constant, rather than using "Name" to have the formatting function applied to the vertices as defined in the graph. That is, the code looks like

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Placed["xxx",Center,rotateLabel]

, which appears to work (rendering each label as xxx). But

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Placed["Name",Center,rotateLabel]

does not work as expected; rotateLabel is not applied to the vertex labels defined in the graph, but rather to the string literal "Name".

A cumbersome way out seems to be to enumerate all vertices and explicitly define the labels in the VertexLabels option as the vertex itself, like

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Graph[vertices,VertexLabels->Map[#->Placed[rotateLabel[#],Center]&,vertices]

. But this seems to me to be a waste of code.

By the way,

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Graph[vertices,VertexLabels->Map[#->Placed[#,Center,rotateLabel]&,vertices]

does not work as expected.

In my application, the vertices are actually permutations in the form of lists of numbers.

Are these shortcomings of Mathematica, or am I doing something wrong?

Thanks,

Tom

[Tom_Verhoeff]

Here is some concrete code to illustrate my question.

The following code works. The vertices are numbers, and these numbers are used as labels, implicitly through "Name".

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Block[{
  vertices = Range[6],
  f = Divisible[#1, #2] || Divisible[#2, #1] &,
  edges},
edges = Select[Subsets[vertices, {2}], f @@ # &];

System`Graph[
  vertices,
  Map[UndirectedEdge @@ # &, edges],
  VertexSize -> .2,
  VertexLabels -> Placed["Name", Center]
  ]
]

If you want to apply custom formatting to the labels, then the following might be expected to work according to the documentation, but it does not work:

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Block[{
  vertices = Range[6],
  f = Divisible[#1, #2] || Divisible[#2, #1] &,
  edges},
edges = Select[Subsets[vertices, {2}], f @@ # &];

System`Graph[
  vertices,
  Map[UndirectedEdge @@ # &, edges],
  VertexShape -> None,
  VertexLabels -> Placed["Name", Center,Framed[#,Background->LightYellow]&]
  ]
]

Instead, you need to attach labels explicitly to each vertex:
Block[{
vertices = Range[6],
f = Divisible[#1, #2] || Divisible[#2, #1] &,
edges},
edges = Select[Subsets[vertices, {2}], f @@ # &];

System`Graph[
vertices,
Map[UndirectedEdge @@ # &, edges],
VertexShape -> None,
VertexLabels ->
Map[# -> Placed[#, Center, Framed[#, Background -> LightYellow] &] &,
vertices]
]
]