2 added 32 characters in body
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edges=Flatten[GatherBy[vrules, Union] /. {Rule[x_,y_],Rule[y_,x_]}:> 
  Property[UndirectedEdge[x,y], 
    EdgeShapeFunction->({Red, Arrowheads[{-.05, .05}], ThickThickness[.01], Arrow@#}&)]];

vertices=Property[#,VertexSize->#2]& @@@ Transpose[{vlist,{"Scaled",#/2} & /@ 
   Normalize[DegreeCentrality[Graph[vlist, vrules]], Total]}];

Graph[vertices, edges, VertexLabels -> Placed["Name", Center],
   GraphLayout -> { "RenderingOrder" -> "EdgeFirst"}, 
   EdgeStyle -> Blue, VertexStyle->White]

Mathematica graphicsMathematica graphics

edges=Flatten[GatherBy[vrules, Union] /. {Rule[x_,y_],Rule[y_,x_]}:> 
  Property[UndirectedEdge[x,y], 
    EdgeShapeFunction->({Red, Arrowheads[{-.05, .05}], Thick, Arrow@#}&)]];

vertices=Property[#,VertexSize->#2]& @@@ Transpose[{vlist,{"Scaled",#/2} & /@ 
   Normalize[DegreeCentrality[Graph[vlist, vrules]], Total]}];

Graph[vertices, edges, VertexLabels -> Placed["Name", Center],
   GraphLayout -> { "RenderingOrder" -> "EdgeFirst"}, VertexStyle->White]

Mathematica graphics

edges=Flatten[GatherBy[vrules, Union] /. {Rule[x_,y_],Rule[y_,x_]}:> 
  Property[UndirectedEdge[x,y], 
    EdgeShapeFunction->({Arrowheads[{-.05, .05}], Thickness[.01], Arrow@#}&)]];

vertices=Property[#,VertexSize->#2]& @@@ Transpose[{vlist,{"Scaled",#/2} & /@ 
   Normalize[DegreeCentrality[Graph[vlist, vrules]], Total]}];

Graph[vertices, edges, VertexLabels -> Placed["Name", Center],
   GraphLayout -> { "RenderingOrder" -> "EdgeFirst"}, 
   EdgeStyle -> Blue, VertexStyle->White]

Mathematica graphics

1
source | link

edges=Flatten[GatherBy[vrules, Union] /. {Rule[x_,y_],Rule[y_,x_]}:> 
  Property[UndirectedEdge[x,y], 
    EdgeShapeFunction->({Red, Arrowheads[{-.05, .05}], Thick, Arrow@#}&)]];

vertices=Property[#,VertexSize->#2]& @@@ Transpose[{vlist,{"Scaled",#/2} & /@ 
   Normalize[DegreeCentrality[Graph[vlist, vrules]], Total]}];

Graph[vertices, edges, VertexLabels -> Placed["Name", Center],
   GraphLayout -> { "RenderingOrder" -> "EdgeFirst"}, VertexStyle->White]

Mathematica graphics