Great stuff. The LinkTrails property does not appear to be documented fully, though. It is used in ref/WolframLanguageData but it is not one of the listed properties in the details section.

When I was teaching Mathematica years ago, I started out with numbers, lists, symbols, patterns, rules, and functions, which I regarded as the fundamental components. I don't know how one would extract that sort of thing from the documentation.

Yes, what we're seeing is the infrastructure. I had no idea there was so much of it.

Where's Mathematica in this? What I see is almost entirely rarely used symbols from what used to be the "add-ons". Mathematica used to be factored rather than presented to the user as a big flat lump. These graphics are an excellent illustration of the fog that now obscures the core functionality. If you want to master Mathematica, this is the stuff you should generally ignore. Only use it when it's applicable to your very specific, specialized problem.

Thanks for doing this Marco! I believe some of this data will help me learn more Mathematica...

Marco, this is amazing :-) Attached is an Interactive Graph of the Wolfram Language Documentation Center that I've created by adding tooltips and hyperlinks to your first CommunityGraph:

g = Graph[Map[Hyperlink[Tooltip[#, DirectedEdge[#[[1]], #[[2]]] &@Flatten[StringCases[{First[#], Last[#]}, "http://reference.wolfram.com/language/ref/" ~~ x__ ~~ ".html" -> x]]], Last[#]] &, DeleteDuplicates[links]]];
communities = FindGraphCommunities[g];
CommunityGraphPlot[g, communities]

This is an excellent way to explore and learn about new functions.

Enjoy!

Attachments:

Actually this is (still) not correct...it needs a custom NearestFunction[]....

My guess is that WRI has the documentation in some custom format that could easily be converted to some "computable" format. Maybe this is not prioritized.

To me, if it were, Information[] would emit something other than null.

A network of the cross-references in the documentation won't help you understand the language itself. How could it make sense of the following?

ffmod[g12_][f_][state[n_, v_, {q1_, q2_}, out_]] := 
 state[n + 1, f[n], {q1 + v - b2q[out], q2 + g12*q1}, q2b[q2 + q1]]

This is part of a simulation of a delta-sigma modulator as an inhomogeneous iterated function system. But you can deconstruct it from the "everything is an expression" viewpoint. Note that b2q and q2b are defined functions, while state is an undefined head.

I hear what you are saying, the replies stating that Mathematica looks for patterns in EXPRESSIONS doesn't mean it can't get from T initai to T final by way of another mesh all points in the complex are connected.

I thought the original goal of the question was to find some meta-data or annotation for each function that would allow a graph of semantically clustered functions to be constructed. Using that meta-data and Nearest[] could facilitate a classification and/or network of those functions..further down that path would be tool-tips with data from Information[] and links into the documentation. So far I cannot see any such meta-data.

I am not sure what you want to do with this info...

Information /@ Take[Names["*Q"], 5]

Turns out there are a lot of pattern tests:

In[3]:= Names["*Q"]

Out[3]= {"AcyclicGraphQ", "AlgebraicIntegerQ", "AlgebraicUnitQ", \
"AntihermitianMatrixQ", "AntisymmetricMatrixQ", "ArgumentCountQ", \
"ArrayQ", "AssociationQ", "AtomQ", "BinaryImageQ", "BipartiteGraphQ", \
"BooleanQ", "BoundaryMeshRegionQ", "BoundedRegionQ", "BusinessDayQ", \
"ByteArrayQ", "ColorQ", "CompatibleUnitQ", "CompleteGraphQ", \
"CompositeQ", "ConnectedGraphQ", "ConstantRegionQ", \
"ContinuousTimeModelQ", "ControllableModelQ", "CoprimeQ", \
"DateObjectQ", "DaylightQ", "DayMatchQ", "DeviceOpenQ", \
"DiagonalizableMatrixQ", "DigitQ", "DirectedGraphQ", "DirectoryQ", \
"DiscreteTimeModelQ", "DisjointQ", "DispatchQ", \
"DistributionParameterQ", "DuplicateFreeQ", "EdgeCoverQ", "EdgeQ", \
"EllipticNomeQ", "EmptyGraphQ", "EulerianGraphQ", "EvenQ", \
"ExactNumberQ", "FileExistsQ", "FreeQ", "FrontEndSharedQ", \
"GeoWithinQ", "GraphQ", "GroupElementQ", "HamiltonianGraphQ", \
"HermitianMatrixQ", "HypergeometricPFQ", "ImageInstanceQ", "ImageQ", \
"IndefiniteMatrixQ", "IndependentEdgeSetQ", "IndependentVertexSetQ", \
"InexactNumberQ", "IntegerQ", "IntersectingQ", "IntervalMemberQ", \
"InverseEllipticNomeQ", "IrreduciblePolynomialQ", "IsomorphicGraphQ", \
"JavaObjectQ", "KEdgeConnectedGraphQ", "KernelSharedQ", "KeyExistsQ", \
"KeyFreeQ", "KeyMemberQ", "KnownUnitQ", "KVertexConnectedGraphQ", \
"LeapYearQ", "LegendreQ", "LetterQ", "LinkConnectedQ", "LinkReadyQ", \
"ListQ", "LoopFreeGraphQ", "LowerCaseQ", "MachineNumberQ", \
"ManagedLibraryExpressionQ", "MandelbrotSetMemberQ", "MarcumQ", \
"MatchLocalNameQ", "MatchQ", "MatrixQ", "MemberQ", "MeshRegionQ", \
"MixedGraphQ", "MultigraphQ", "NameQ", "NegativeDefiniteMatrixQ", \
"NegativeSemidefiniteMatrixQ", "NormalMatrixQ", "NumberQ", \
"NumericQ", "ObservableModelQ", "OddQ", "OptionQ", "OrderedQ", \
"OrthogonalMatrixQ", "OutputControllableModelQ", "PacletNewerQ", \
"PartitionsQ", "PathGraphQ", "PermutationCyclesQ", \
"PermutationListQ", "PlanarGraphQ", "PolynomialQ", \
"PositiveDefiniteMatrixQ", "PositiveSemidefiniteMatrixQ", \
"PossibleZeroQ", "PrimePowerQ", "PrimeQ", "PrintableASCIIQ", \
"ProcessParameterQ", "QHypergeometricPFQ", "QuadraticIrrationalQ", \
"QuantityQ", "RegionQ", "RegularlySampledQ", "RootOfUnityQ", \
"SameObjectQ", "SameQ", "SatisfiableQ", "SimpleGraphQ", \
"SquareFreeQ", "SquareMatrixQ", "StringContainsQ", "StringEndsQ", \
"StringFreeQ", "StringMatchQ", "StringQ", "StringStartsQ", "SubsetQ", \
"SymmetricMatrixQ", "SyntaxQ", "TautologyQ", "TensorQ", \
"TimeObjectQ", "TreeGraphQ", "TrueQ", "UnateQ", "UndirectedGraphQ", \
"UnitaryMatrixQ", "UnsameQ", "UpperCaseQ", "URLExistsQ", "ValueQ", \
"VectorQ", "VertexCoverQ", "VertexQ", "WeaklyConnectedGraphQ", \
"WeightedGraphQ"}

In[4]:= Length[%]

Out[4]= 157

I haven't figured out how get their definitions all at once. The following doesn't work:

(? #)& /@ Names["*Q"]