g=Graph[Table[j->FromDigits[Drop[IntegerDigits[j,2],1],2]+1,{j,2,2^5-1}],GraphStyle->"ThickEdge",GraphLayout->"RadialDrawing"]

rg=RandomGraph[{31,70},VertexStyle->Red,AbsoluteOptions[g,VertexCoordinates]]

Show[g,rg]