@yode's answer is the better choice, but since it missed some options, here is a manual one that works in this particular case.
The question you asked was discussed during a Live CEOing session (I don't remember the episode). From version 10.2 we have WolframLanguageData
which in this particular case, if we assume each option was used in the documentation examples, we can somehow extract them.
The code is:
list1 =
Cases[Cases[
WolframLanguageData["GraphLayout",
"DocumentationExampleInputs"], {___, "GraphLayout", "\[Rule]",
a__} :> ReplaceAll[ToExpression@{a}, Null -> Nothing],
Infinity], {a_String, ___} :> a, Infinity] // DeleteDuplicates //
Sort
(* Out: {"BalloonEmbedding", "BipartiteEmbedding", "CircularEmbedding",
"CircularMultipartiteEmbedding", "DiscreteSpiralEmbedding",
"GravityEmbedding", "GridEmbedding", "HighDimensionalEmbedding",
"LayeredDigraphDrawing", "LayeredDigraphEmbedding",
"LayeredEmbedding", "LinearEmbedding", "MultipartiteEmbedding",
"PlanarEmbedding", "RadialEmbedding", "RandomEmbedding",
"SpectralEmbedding", "SphericalEmbedding", "SpiralEmbedding",
"SpringElectricalEmbedding", "SpringEmbedding", "StarEmbedding",
"TutteEmbedding"} *)
@yode answer (\"
was removed from options):
yode = StringReplace[
ResourceFunction["QueryCodeCompletion"]["GraphLayout",
"KernelSymbol", "Graph", "InOptionValuePosition"], "\"" -> ""]
(* Out: {"SpringElectricalEmbedding", "SpringEmbedding",
"HighDimensionalEmbedding", "LayeredEmbedding",
"LayeredDigraphEmbedding", "BalloonEmbedding", "RadialEmbedding",
"SpiralEmbedding", "BipartiteEmbedding", "CircularEmbedding",
"CircularMultipartiteEmbedding", "DiscreteSpiralEmbedding",
"GridEmbedding", "LinearEmbedding", "MultipartiteEmbedding",
"PlanarEmbedding", "StarEmbedding", "SpectralEmbedding",
"TutteEmbedding", "GraphLayout", "Graph"} *)
Comparison
(* options exist in yode but not in list1 *)
Complement[yode, list1]
(* Out: {"Graph", "GraphLayout"} *)
(* options exist in list1 but not in yode *)
Complement[list1, yode]
(* Out: {"GravityEmbedding", "LayeredDigraphDrawing", "RandomEmbedding", "SphericalEmbedding"} *)
An interesting point is that all the options end with Embedding
except "LayeredDigraphDrawing"
(the option used in an example in the "LayeredDigraphEmbedding"
section).