Mathematica 1024 chars
Graph[Partition[ Riffle[Characters[ StringTake[ElementData[][[2]], 3] <> StringTake[WordData["high", "Antonyms"][[2, 2, 1]], 2] <> FromCharacterCode[Power[2, 5]] <> StringTake[GraphData[][[Prime@705]], 2] <> StringTake[AstronomicalData["Planet"][[1]], {3}] <> "ld"], Rest@Characters[ StringTake[ElementData[][[2]], 3] <> StringTake[WordData["high", "Antonyms"][[2, 2, 1]], 2] <> FromCharacterCode[Power[2, 5]] <> StringTake[GraphData[][[Prime[705]]], 2] <> StringTake[AstronomicalData["Planet"][[1]], {3}] <> "ld"]], 2] /. {a_, b_} :> DirectedEdge[a, b], EdgeLabelStyle -> Power[2, 4], EdgeLabels -> (Partition[ Riffle[l = Characters[ StringTake[ElementData[][[2]], 3] <> StringTake[WordData["high", "Antonyms"][[2, 2, 1]], 1 + 1] <> FromCharacterCode[Sqrt[Sqrt[1048576]]] <> StringTake[GraphData[][[Prime[705]]], 2] <> StringTake[AstronomicalData["Planet"][[1]], {3}] <> "ld"], Rest@l], 2] /. {a_, b_} :> DirectedEdge[a, b]) + Power[{1, 8, 27, 64, 125, 216, 343, 512, 729, 1000}, 1/3] /. {Plus[a_, b_] :> Rule[b, a]}, VertexLabelStyle -> Directive[RGBColor[0, 0, 1], Large], VertexLabels -> "Name", ImagePadding -> Power[5, 2], ImageSize -> 2^2*5^2*7]

De-bowled (partially)
For those who don't have access to Mathematica's curated data:
ElementData[][[2]] WordData["high", "Antonyms"][[2, 2, 1]] GraphData[][[Prime[705]]] AstronomicalData["Planet"][[1]]
"Helium"
"low"
"WongGraph"
"Mercury"
"Hel" (from "Helium") + "lo" (from "low") + " " (FromCharacterCode[32]) + "Wo" (from "WongGraph") + "r" (from "Mercury") + "ld"
yields the string "Hello World".
The string is split into characters, each of which becomes a vertex in the following graph:
Graph[{"H" \[DirectedEdge] "e", "e" \[DirectedEdge] "l", "l" \[DirectedEdge] "l", "l" \[DirectedEdge] "o", "o" \[DirectedEdge] " ", " " \[DirectedEdge] "W", "W" \[DirectedEdge] "o", "o" \[DirectedEdge] "r", "r" \[DirectedEdge] "l", "l" \[DirectedEdge] "d"}, EdgeLabelStyle -> 16, EdgeLabels -> {"H" \[DirectedEdge] "e" -> 1, "e" \[DirectedEdge] "l" -> 2, "l" \ [DirectedEdge] "l" -> 3, "l" \[DirectedEdge] "o" -> 4, "o" \[DirectedEdge] " " -> 5, " " \[DirectedEdge] "W" -> 6, "W" \[DirectedEdge] "o" -> 7, "o" \[DirectedEdge] "r" -> 8, "r" \[DirectedEdge] "l" -> 9, "l" \[DirectedEdge] "d" -> 10}, VertexLabelStyle -> Directive[Blue, Large], VertexLabels -> "Name", ImagePadding -> 25]