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Given the following directed graphs:

ClearAll[one, two];
one = {1 -> 2, 1 -> 3, 3 -> 4, 4 -> 1};
two = {1 -> 2, 1 -> 3, 1 -> 4};

I generate a single directed graph by:

Graph[Join[one, two], VertexLabels -> "Name"]

It is fine. When I assign different colors for each graph like Blue for one and Red for two and ask for a layered graph plot, it does not work! I tried EdgeAdd, GraphUnion but no success. Any idea about the feasibility of such a custom-designed graph? I also consulted with IGraphM, hoping that it might have developed the code I am after, but again no success.

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2 Answers 2

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Add colors as tags to the edges:

taggededges = MapIndexed[DirectedEdge @@ 
   Append[List @@ #, 
    If[#2[[1]] <= Length@one, Red, Blue]] &] @ 
  Join[one, two]

enter image description here

Graph[taggededges, VertexLabels -> "Name", 
 EdgeStyle -> {DirectedEdge[a_, b_, c_] :> c}]

enter image description here

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  • 1
    $\begingroup$ Thanks as usual for your excellent code. My depository of MMA codes are full of yours! $\endgroup$ Jan 28, 2023 at 18:20
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ClearAll[one, two];
one = {1 -> 2, 1 -> 3, 3 -> 4, 4 -> 1};
two = {1 -> 2, 1 -> 3, 1 -> 4};

Legended[
 Graph[Join[
   Style[#, Magenta] & /@ Intersection[one, two],
   Style[#, Blue] & /@ Complement[one, two],
   Style[#, Red] & /@ Complement[two, one]], 
  VertexLabels -> "Name"],
 Placed[
  LineLegend[{Blue, Magenta, Red}, {"one", "one && two", "two"}],
  {.3, .8}]]

enter image description here

EDIT: Inspired by @kglr's excellent answer. A form which is easier for me to understand:

Legended[
 Graph[
  Join[
   one /. (x_ -> y_) ->
     Style[DirectedEdge[x, y, ""], Blue],
   two /. (x_ -> y_) ->
     Style[DirectedEdge[x, y], Red]]],
 Placed[
  LineLegend[{Blue, Red}, {"one", "two"}],
  {.3, .8}]]

enter image description here

EDIT 2: For a LayeredGraphPlot

Legended[
 LayeredGraphPlot[
  Join[
   one /. (x_ -> y_) -> Style[
      DirectedEdge[x, y, ""], Blue],
   two /. (x_ -> y_) -> Style[
      DirectedEdge[x, y], Red]],
  PlotTheme -> "NameLabeled"],
 Placed[LineLegend[{Blue, Red},
   {"one", "two"}], {.3, .3}]]

enter image description here

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  • $\begingroup$ Thanks a lot for your effort and answers. I can follow your answer with my limited knowledge of programming. kglr's excellent answer is certainly way beyond my programming boundary. $\endgroup$ Jan 28, 2023 at 18:19
  • $\begingroup$ This is not a request but a note. Using kglr's code, I can generate a layered graph easily by : LayeredGraphPlot[taggededges, VertexLabels -> "Name", EdgeStyle -> {DirectedEdge[a_, b_, c_] :> c}, ImageSize -> 350]. I tried some versions of your code to do the same but could not do it. $\endgroup$ Jan 28, 2023 at 18:32
  • $\begingroup$ Very nice! I tried it before writing you but somehow it did not work. It seems that I made a mistake somewhere. Thank you very much for the code. $\endgroup$ Jan 28, 2023 at 20:21

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