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I would like to obtain entrance edge and output edges as in the following figure enter image description here

My code is the following:

vertices = vertices = {"S", "E", "I", "R"};
groups = {{"S"}, {"E", "I"}, {"R"}};
colors = Flatten@
   MapThread[Thread@*Rule, {groups, {White, Yellow, Red}}];



chart = LayeredGraphPlot[{Style[Labeled["S" -> "E", F], Red, Thick], 
   Style[Labeled["E" \[UndirectedEdge] "S", \[Beta]], Dashed, Green, 
    Thick], Style[Labeled["E" -> "I", Subscript[\[Gamma], e]], Brown, 
    Thick], Style[Labeled["I" -> "R", Subscript[\[Gamma], i] ], 
    Dashed, Purple, Thick], 
   Style[Labeled["R" -> "S", Subscript[\[Gamma], r] ], Dashed, Cyan, 
    Thick], Style[Labeled["S" -> "R", Subscript[\[Gamma], s] ], 
    Dashed, Purple, Thick]}, Left, 
  PlotStyle -> {"TemperatureMap", Bold},
  VertexLabels -> Placed[Automatic, Center], 
  PerformanceGoal -> "Quality",
  {VertexShapeFunction -> {"S" -> "Square", 
     "R" -> "ConcaveHexagon"}}, VertexStyle -> colors, 
  VertexShapeFunction -> ({EdgeForm[Black], Disk[#1, 0.2], 
      Text[#2, #1]} &), VertexSize -> Large, 
  EdgeLabelStyle -> Directive[10, Background -> White]]

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 edges = {Style[Labeled["S" -> "E", F], Red, Thick], 
   Style[Labeled["E" \[UndirectedEdge] "S", β], Dashed, Green, Thick], 
   Style[Labeled["E" -> "I", Subscript[γ, e]], Brown,Thick], 
   Style[Labeled["I" -> "R", Subscript[γ, i]], Dashed, Purple, Thick], 
   Style[Labeled["R" -> "S", Subscript[γ, r]], Dashed, Cyan, Thick], 
   Style[Labeled["S" -> "R", Subscript[γ, s]], Dashed, Purple, Thick]};

You can add new edges and use None as VertexShapeFunction to make some vertices invisible:

invisiblevertices = {"Eb", "Ib", "Rb", "Sb"};

newedges = {"Sb" -> "S", "R" -> "Rb", "I" -> "Ib", "E" -> "Eb"};

newedgelabels = {μ, μR, μI, μE};

edges2 = Join[edges, MapThread[Labeled, {newedges, newedgelabels}]];

options = { VertexLabels -> {_ -> Placed[Automatic, Center], 
       Alternatives @@ invisiblevertices -> None}, 
    VertexShapeFunction -> {"S" -> "Square", "R" -> "ConcaveHexagon", 
       Alternatives @@ invisiblevertices -> None},
    VertexStyle -> colors, VertexSize -> Large, ImageSize -> 700,
    PerformanceGoal -> "Quality", 
    EdgeLabelStyle -> Directive[10, Background -> White]};
 
LayeredGraphPlot[edges2, Left, options]

enter image description here

LayeredGraphPlot[edges2, Left, options , 
  EdgeShapeFunction -> {("E" -> "Eb") -> (Arrow[{#[[1]], #[[1]] + {0, -1}}] &), 
     ("I" -> "Ib") -> (Arrow[{#[[1]], #[[1]] + {0, -1}}] &)}]

enter image description here

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  • $\begingroup$ Thanks a lot!! :) This is what I really wanted! $\endgroup$ – Rim ADENANE Jun 7 at 8:37

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