How to draw the classic state diagram using Mathematica?

Question

Is it possible and practical for Mathematica to draw something like this (being created by Graphviz):

This is the best that I can get (but the shape and style are not satisfying):

Code:

GraphPlot[{{A -> C, "go"}, {C -> B, "gone"}, {C -> D, 
   "went"}, {C -> C, "loop"}}, VertexLabeling -> True, 
 DirectedEdges -> True]

Answer 1

You can do something like this using VertexRenderingFunction.

GraphPlot[{{A -> C, "go"}, {C -> B, "gone"}, {C -> D, "went"}, {C -> C, "loop"}}, 
 DirectedEdges -> True, 
 VertexRenderingFunction -> ({{White, Disk[#, 0.15]}, 
     AbsoluteThickness[2], Circle[#, 0.15], 
     If[MatchQ[#2, A | B], Circle[#, 0.12], {}], Text[#2, #]} &)]

---

Method Updated February 2015

To preserve the ability to interactively rearrange the graph with the drawing tools (double click) one must keep the vertex graphics inside of GraphicsComplex, with indexes rather than coordinates. I believe one could do this from VertexRenderingFunction using an incrementing variable but it seems easier an possibly more robust to do it with post-processing. This works in versions 7 and 10 of Mathematica, presumably 8 and 9 as well:

GraphPlot[
  {{A -> C, "go"}, {C -> B, "gone"}, {C -> D, "went"}, {C -> C, "loop"}},
  DirectedEdges -> True
] /.
 Tooltip[Point[n_Integer], label_] :>
   {{White, Disk[n, 0.15]},
    Black, AbsoluteThickness[2], Circle[n, 0.15], 
    If[MatchQ[label, A | B], Circle[n, 0.12], {}], Text[label, n]}

Answer 2

There's no need for interactive placement to get your vertices at the desired location as mr.Wizard suggests in his answer. You can use VertexCoordinateRules for that:

GraphPlot[{{A -> C, "go"}, {C -> B, "gone"}, {C -> D, "went"}, {C -> C, "loop"}}, 
    DirectedEdges -> True, 
    VertexRenderingFunction -> 
          ({{White, Disk[#, 0.15]}, AbsoluteThickness[2], Circle[#, 0.15], 
           If[MatchQ[#2, A | B], Circle[#, 0.12], {}], Text[#2, #]} &),
    VertexCoordinateRules -> 
          {A -> {0, 0}, C -> {0.75, 0},B -> {1.5, 0.25}, D -> {1.5, -0.25}}
]