Problem in coloring network links with linear gradients through VertexColors

Question

I am trying to plot a network with colored links and nodes. I would like to color links with a gradient depending on the colors of its endpoints/nodes. For instance, a link between a blue and a red node should have a linear gradient between blue and red. I would also like for links to be curved so a I am using also a BezierCurve function.

In order to obtain the gradient on the BezierCurve I am using VertexColors, which however works only on the Line graphics. So what I am doing is: for every couple of nodes get their coordinates, interpolate and create a BezierFunction, run the BezierFunction over an evenly split range and get a collection of lines approximating a BezierCurve, then color the lines.

However, I am unable to obtain colored links and would like to know where is the problem. The code is this one:

 versiz = {1 -> 0.8317766166719344`, 2 -> 0.7193685818395111`, 
   3 -> 0.6238324625039507`, 4 -> 0.7917171988845775`, 
   5 -> 0.769484807238461`, 6 -> 0.6907755278982137`, 
   7 -> 0.583773044716594`, 8 -> 0.48283137373023005`, 
   9 -> 0.48283137373023005`, 10 -> 0.48283137373023005`, 
   11 -> 0.48283137373023005`, 12 -> 0.4158883083359672`, 
   13 -> 0.48283137373023005`, 14 -> 0.5375278407684164`, 
   15 -> 0.4158883083359672`, 16 -> 0.4158883083359672`, 
   17 -> 0.5375278407684164`, 18 -> 0.4158883083359672`, 
   19 -> 0.4158883083359672`, 20 -> 0.4158883083359672`};
cols = Table[If[RandomReal[] < 0.3, Red, Blue], {i, 1, 20}];

edges = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7}, {1, 8}, {1, 
    9}, {1, 10}, {1, 11}, {1, 14}, {1, 15}, {1, 16}, {1, 18}, {1, 
    19}, {1, 20}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 7}, {2, 10}, {2,
     11}, {2, 12}, {2, 13}, {2, 20}, {3, 4}, {3, 5}, {3, 6}, {3, 
    8}, {3, 9}, {3, 13}, {4, 5}, {4, 6}, {4, 10}, {4, 11}, {4, 
    12}, {4, 13}, {4, 14}, {4, 15}, {4, 16}, {4, 17}, {4, 18}, {5, 
    7}, {5, 8}, {5, 9}, {5, 12}, {5, 14}, {5, 15}, {5, 17}, {5, 
    18}, {5, 19}, {6, 7}, {6, 9}, {6, 11}, {6, 13}, {6, 16}, {6, 
    20}, {7, 8}, {7, 15}, {7, 19}, {8, 10}, {9, 17}, {10, 12}, {11, 
    18}, {13, 14}, {14, 16}, {14, 17}, {17, 19}, {17, 20}};

    Graph[UndirectedEdge @@@ edges, 
 EdgeShapeFunction -> ({AbsoluteThickness[4], 
     Line[BezierFunction[{#1[[1]], #1[[1]] + 
          0.5 RotationMatrix[.3].(#1[[2]] - #1[[1]]), #1[[2]]}] /@ 
       Range[0, 1, 0.1], 
      VertexColors -> (Blend[cols[[List @@ #2]], #] & /@ 
         Range[0, 1, 0.1])]} &), VertexSize -> versiz, 
 VertexStyle -> Thread[Range[VertexCount[net]] -> cols]]

I am afraid that the Blend function is not working properly here. If I substitute #2 with fixed colors, I do get colored links (although they are static):

 Graph[UndirectedEdge @@@ edges, 
     EdgeShapeFunction -> ({AbsoluteThickness[4], 
         Line[BezierFunction[{#1[[1]], #1[[1]] + 
              0.5 RotationMatrix[.3].(#1[[2]] - #1[[1]]), #1[[2]]}] /@ 
           Range[0, 1, 0.1], 
          VertexColors -> (Blend[{Red, Blue}, #] & /@ 
             Range[0, 1, 0.1])]} &), VertexSize -> versiz, 
     VertexStyle -> Thread[Range[20] -> cols]]

Answer 1

You have a nested pure-function, both levels of which use Slot:

({AbsoluteThickness[4], 
   Line[BezierFunction[{#1[[1]], #1[[1]] + 
        0.5 RotationMatrix[.3].(#1[[2]] - #1[[1]]), #1[[2]]}] /@ 
     Range[0, 1, 0.1], 
    VertexColors -> (Blend[cols[[List @@ #2]], #] & /@ 
       Range[0, 1, 0.1])]} &)

You intend for the #2 to bind to the outer &, but it instead binds to the inner &. For situations like this, you can change one of these to a Function with named arguments:

Graph[UndirectedEdge @@@ edges, 
 EdgeShapeFunction -> ({AbsoluteThickness[4], 
     Line[BezierFunction[{#1[[1]], #1[[1]] + 
          0.5 RotationMatrix[.3].(#1[[2]] - #1[[1]]), #1[[2]]}] /@ 
       Range[0, 1, 0.1], 
      VertexColors -> (Function[val, Blend[cols[[List @@ #2]], val]] /@
          Range[0, 1, 0.1])]} &), VertexSize -> versiz, 
 VertexStyle -> Thread[Range[20] -> cols]]