Colorized Graphs

ERF[weights_]:={

ColorData["BrightBands"][Rescale[weights[[Sequence@@#2]],
{Min@weights,Max@weights}]],

Thickness[0.01],Opacity[0.75],Arrow[#1]}&;
GP[weights_]:=GraphPlot[

WeightedAdjacencyGraph[weights],
Method -> "StarEmbedding",VertexStyle->LightGray,
VertexSize->.15,VertexShapeFunction->"ConcaveHexagon",
EdgeRenderingFunction->(ERF[weights]),ImageSize->500]
GP[SparseArray[{i_,j_}:>i+j,{9,9}]]