I post this for illustrative purposes (if I have understood underlying aim correctly).

f[n_] := {DirectedEdge[##], Boole[Divisible[##]]} & @@@ Tuples[Range[2, n], 2]
g[n_] := With[{ds = Transpose@f[n]},
           Graph[##, 
           VertexLabels -> Thread[Range[2, n] -> (Placed[Framed[#, Background -> White], Center] & /@ 
           Range[2, n])],
           VertexLabelStyle -> Red, 
           EdgeLabels -> "EdgeWeight",
           EdgeStyle -> MapThread[Function[{u, v}, u -> {RGBColor[v, 0, 0], Thickness[0.005 + v 0.005]}], {#1, 
           ds[[2]]}]] & @@ ({#1, EdgeWeight -> #2} & @@ ds)]

Using:

Grid[Partition[g /@ Range[2, 10], 3], Frame -> All]