Jaebum,

Your solution is pretty smart (and rather tricky too); it works after adding new edges with new colours.

Now I am traying to attatch hyperlinks to the edges but before I need a complete understanding of the structure of your construct.

I will be back with the full solution, adding tooltips and/or hyperlinks, if am able to make it.

Martin.

Here's one can be considered:

colorFuncSet[edge_, clist_] := 
 With[{a = Unique["x"]}, {Inactive[a], 
   Inactive[edge -> (a = 0; {a++; clist[[a]], Arrow[#]} &)]}]

SetColorFunction[edgeset_] :=
 Block[{gather},
  gather = 
   colorFuncSet[#[[1, 1]], #[[All, 2]]] & /@ GatherBy[edgesets, First];
  (With[{var = gather[[All, 1]], cont = gather[[All, 2]]}, 
     Hold@Module[var, cont]] /. Inactive[x_] :> x)
  ]

Example:

edgesets = {"P" \[DirectedEdge] "M" -> RGBColor[1, 0, 0], 
   "M" \[DirectedEdge] "P" -> RGBColor[1, 0, 0], 
   "P" \[DirectedEdge] "Q" -> RGBColor[1, 0, 0], 
   "Q" \[DirectedEdge] "M" -> RGBColor[1, 0, 0], 
   "M" \[DirectedEdge] "V" -> RGBColor[0, 0, 1], 
   "V" \[DirectedEdge] "M" -> RGBColor[0, 0, 1], 
   "P" \[DirectedEdge] "V" -> RGBColor[0, 0, 1], 
   "Q" \[DirectedEdge] "V" -> RGBColor[0, 0, 1], 
   "V" \[DirectedEdge] "P" -> RGBColor[0, 0, 1], 
   "V" \[DirectedEdge] "Q" -> RGBColor[0, 0, 1], 
   "P" \[DirectedEdge] "Q" -> RGBColor[0.5, 0, 0.5], 
   "Q" \[DirectedEdge] "M" -> RGBColor[0.5, 0, 0.5], 
   "M" \[DirectedEdge] "Q" -> RGBColor[0.5, 0, 0.5], 
   "P" \[DirectedEdge] "V" -> RGBColor[0.5, 0, 0.5], 
   "V" \[DirectedEdge] "Q" -> RGBColor[0.5, 0, 0.5], 
   "M" \[DirectedEdge] "V" -> RGBColor[0.5, 0, 0.5]};

coloredges = SetColorFunction[edgesets];
MVPQGraph = 
  Graph[{"M", "V", "P", "Q"}, edgesets[[All, 1]], 
   VertexSize -> .09*(5/3),  
   VertexLabels -> 
    Placed["Name", Center],  (*EdgeLabels\[Rule]edgelabels ,*)
   VertexShapeFunction -> "RoundedSquare", 
   VertexStyle -> Hue[0.125, 0.7, 0.9], 
   VertexLabelStyle -> Directive[Bold, FontFamily -> "Arial", 12], 
   EdgeStyle -> Arrowheads[{{.03 , .3}}], 
   EdgeShapeFunction -> ReleaseHold[coloredges]]