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Consider the following code:

vsh[{xc_, yc_}, name_, {w_, h_}] := {LightYellow, 
   Rectangle[{xc - w, yc - h}, {xc + w, yc + h}], 
   Inset[Style[Text[name], 14, Black, Bold], {xc, yc}]};
options = 
  Sequence[VertexSize -> 0.1, VertexShapeFunction -> vsh, 
   GraphLayout -> "CircularEmbedding", ImageSize -> 350, 
   EdgeStyle -> Blue];

g1 = Graph[{1 -> 2, 1 -> 3, 2 -> 4, 3 -> 4}, options];
g1

The output will be a simple graph with vertex labels depicted in rectangles (as can be inferred from vsh):

Mathematica output

My question is: how can I encapsulate the vertex labels in circles instead? Nothing I've tried seems to be working.

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    $\begingroup$ try changing Rectangle[...] to Disk[{xc, yc}, Min[w, h]] or use any other function of w and h to control the radius. $\endgroup$ – kglr Sep 28 '12 at 0:46
  • $\begingroup$ @kguler Thank you very much, this worked. $\endgroup$ – arshajii Sep 28 '12 at 0:53
  • $\begingroup$ A.R.S. my pleasure. It is always fun to play with custom shape function. I posted an alternative way to get the same result using options VertexStyle, VertexLabels and VertexLabelStyle. $\endgroup$ – kglr Sep 28 '12 at 1:32
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You can change Rectangle[...] to Disk[{xc, yc}, Min[w, h]] or use any other function of w and h to control the disk radius.

But ... you can also get the same result without having to define a custom VertexShapeFunction using the options:

options = Sequence[VertexStyle -> LightYellow,
   VertexSize -> 0.15,
   VertexLabels -> Placed["Name", Center], 
   VertexLabelStyle -> Directive[20, Red, Bold, Italic], 
   GraphLayout -> "CircularEmbedding", ImageSize -> 350, 
   EdgeStyle -> Blue];

Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, options]

enter image description here

You can also use the option PlotTheme -> "IndexLabeled" in versions 12.0+:

Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, PlotTheme -> "IndexLabeled", 
 VertexStyle -> Yellow, VertexSize -> Medium, 
 VertexLabelStyle -> Directive[Italic, 16], EdgeStyle -> Blue]

enter image description here

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  • $\begingroup$ Placed["Name", Center] works too. $\endgroup$ – Szabolcs Dec 30 '17 at 11:02
  • $\begingroup$ @Szabolcs, yes, thank you. Made the change. $\endgroup$ – kglr Dec 30 '17 at 11:05
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According to google you are supposed to use VertexRenderingFunction.

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    $\begingroup$ Not too sure, but I think that works with GraphPlot, not with Graph... $\endgroup$ – cormullion Sep 28 '12 at 17:46
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Try:

Rectangle[{xc - w, yc - h}, {xc + w, yc + h}, RoundingRadius -> 1000]

Rounded corners rather than circles can be had with smaller values.

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