Graph (network) styling: avoid vertices and edges overlapping

Question

Is there a way to avoid the edges and vertices 'overlapping' in a graph with custom styling? That is, the edges should stop once they reach the 'border' of the shape representing the vertex (in this case, an ellipse). Here's what I get now:

And here is how I called Graph (here transitionRules represents a list of rules):

Graph[transitionRules, 

  VertexLabels -> Table[i[[1]] -> Placed[Style[i[[1]], Bold, 10], Center], {i,transitionRules}],
  VertexSize ->Table[Which[i[[2]] >= 1.6, i[[1]] -> 1.6,  i[[2]] <= 0.6,i[[1]] -> 0.6, True, i], {i, nOfCases}],
  GraphLayout -> "RadialEmbedding",
  EdgeStyle -> Join[Table[(transitionRules[[i]]) -> Thickness[weights[[i]]], {i, Length@transitionRules}], {Opacity[0.5, Blue]}],
  VertexShape ->Graphics[{ Opacity[0.6, Hue[0.53, 0.27, 1]], EdgeForm[Blue],Ellipsoid[{0, 0}, {8, 4}]}]]
 ]

Here is the data in transitionRules:

{"C-M" -> "D-Dom7", "D-Dom7" -> "G-Dom7", "G-Dom7" -> "C-M", 
 "C-M" -> "A-m", "A-m" -> "D-Dom7", "D-Dom7" -> "G-M", 
 "G-M" -> "C-M7M", "C-M7M" -> "A-Dom7", "A-Dom7" -> "D-Dom7", 
 "G-M" -> "E-d7d", "E-d7d" -> "D-m", "D-m" -> "D-d7d", 
 "D-d7d" -> "C-M", "C-M" -> "F-M7M", "F-M7M" -> "D-Dom7", 
 "C-M" -> "C-Dom7", "C-Dom7" -> "F-M7M", "F-M7M" -> "F#/G\[Flat]-d7d",
  "F#/G\[Flat]-d7d" -> "C-m7M", "C-m7M" -> "F-d7d", 
 "F-d7d" -> "G-Dom7", "C-M" -> "G-Dom7", "G-Dom7" -> "C-d7d", 
 "C-d7d" -> "C-M", "G-Dom7" -> "C-Dom7", "C-Dom7" -> "F-M", 
 "F-M" -> "D-Dom7"}

Answer 1

You better use VertexShapeFunction than VertexShape option for this and set PerformanceGoal -> "Quality". Also you might need to tweak VertexSize computation:

Graph[transitionRules, 
 VertexLabels -> 
  Table[i[[1]] -> Placed[Style[i[[1]], Bold, 10], Center], {i, 
    transitionRules}], 
 VertexSize -> 
  Thread[nOfCases[[All, 1]] -> 
    Rescale[nOfCases[[All, 2]], 
     MinMax[nOfCases[[All, 2]]], {0.3, 0.6}]], 
 GraphLayout -> "RadialEmbedding", 
 EdgeStyle -> 
  Join[Table[(transitionRules[[i]]) -> Thickness[weights[[i]]], {i, 
     Length@transitionRules}], {Opacity[0.5, Blue]}],
 VertexStyle -> 
  Directive[Opacity[0.6, Hue[0.53, 0.27, 1]], EdgeForm[Blue]], 
 VertexShapeFunction -> (Ellipsoid[#1, {2, 1} #3] &), 
 PerformanceGoal -> "Quality"]