Database of labelled simple graphs on $n$-vertices? Recently for fun, I have been doing some computational experiments in maple with graphs and have suddenly desired a collection of labelled simple graphs on $n$-vertices. I am aware of Brenden Mckay's collection of unlabelled simple graphs and his program geng but have not found something similar for labelled graphs. I imagine it would only be tractable for smaller numbers of vertices but I am still interested. 
In theory, it should be a much simpler problem to generate labelled graphs on $n$ vertices but for some reason, I can't think of how to effectively program it in maple. (Any hints in this direction would also be much appreciated.)
 A: For completeness, @MishaLavrov has a solution (below), which with slight modification gives the labeled graphs:
Graph[Range[n], #, VertexLabels->Automatic] & /@ Subsets[UndirectedEdge @@@ Subsets[Range[n], {2}]]

So if n=3 we get

Moreover, Mathematica has a curated database of graphs (GraphData[]), with excellent tools for creating and classifying them:

Here's just a list of the graph classes:
{"Acyclic", "AlmostHamiltonian", "AlternatingGroup", "Andrasfai",
"Antelope", "Antiprism", "Apex", "Apollonian", "Archimedean",
"ArchimedeanDual", "ArcTransitive", "Arrangement", "Asymmetric",
"BananaTree", "Barbell", "Beineke", "Bicolorable", "Biconnected",
"Bicubic", "Bipartite", "BipartiteKneser", "Bishop", "BlackBishop",
"Book", "Bouwer", "Bridged", "Bridgeless", "Cactus", "Cage",
"Caterpillar", "Caveman", "Cayley", "Centipede", "Chang", "Chordal",
"Chordless", "ChromaticallyNonunique", "ChromaticallyUnique",
"Circulant", "Class1", "Class2", "ClawFree", "CocktailParty",
"Complete", "CompleteBipartite", "CompletelyRegular", "CompleteTree",
"CompleteTripartite", "Cone", "Conference", "Connected",
"CriticalNonplanar", "CrossedPrism", "Crown", "CubeConnectedCycle",
"Cubic", "Cycle", "Cyclic", "Cyclotomic", "DeterminedByResistance",
"DeterminedBySpectrum", "Disconnected", "DistanceRegular",
"DistanceTransitive", "Doob", "DutchWindmill", "EdgeTransitive",
"Empty", "Eulerian", "Fan", "FibonacciCube", "Firecracker",
"Fiveleaper", "FoldedCube", "Forest", "Fullerene", "Fusene", "Gear",
"GeneralizedPetersen", "GeneralizedPolygon", "Grid", "Haar",
"Hadamard", "Halin", "HalvedCube", "HamiltonConnected",
"HamiltonDecomposable", "Hamiltonian", "HamiltonLaceable", "Hamming",
"Hanoi", "Harary", "Helm", "HoneycombToroidal", "HStarConnected",
"Hypercube", "Hypohamiltonian", "Hypotraceable", "Identity",
"IGraph", "Imperfect", "Incidence", "Integral", "Johnson", "Keller",
"KempeCounterexample", "King", "Kneser", "Knight", "Kuratowski",
"Ladder", "LadderRung", "LCF", "Line", "Lobster", "Local",
"LocallyPetersen", "Lollipop", "Matchstick",
"MaximallyNonhamiltonian", "Median", "MengerSponge", "Metelsky",
"MoebiusLadder", "MongolianTent", "Moore", "Mycielski", "Noncayley",
"Nonempty", "Noneulerian", "Nonhamiltonian", "Nonplanar",
"Nonsimple", "NoPerfectMatching", "NotDeterminedByResistance",
"NotDeterminedBySpectrum", "Nuciferous", "Octic", "Odd", "Ore",
"Paley", "Pan", "Pancyclic", "Path", "Paulus", "Perfect",
"PerfectMatching", "PermutationStar", "Planar", "Platonic",
"Polyhedral", "Polyiamond", "Polyomino", "Prism", "Pseudoforest",
"Pseudotree", "Quartic", "Queen", "Quintic", "Regular",
"RegularPolychoron", "Rook", "RookComplement", "SelfComplementary",
"SelfDual", "Semisymmetric", "Septic", "Sextic", "SierpinskiCarpet",
"SierpinskiSieve", "SierpinskiTetrahedron", "Simple", "Snark",
"Spider", "SquareFree", "StackedBook", "StackedPrism", "Star",
"StronglyPerfect", "StronglyRegular", "Sun", "Sunlet", "Symmetric",
"Tadpole", "Taylor", "Tetrahedral", "Toroidal", "TorusGrid",
"Traceable", "Transposition", "Tree", "TriangleFree", "Triangular",
"TriangularGrid", "TriangularHoneycombAcuteKnight",
"TriangularHoneycombBishop", "TriangularHoneycombKing",
"TriangularHoneycombObtuseKnight", "TriangularHoneycombQueen",
"TriangularHoneycombRook", "Triangulated", "Tripod", "Turan",
"TwoRegular", "Unicyclic", "UnitDistance", "Untraceable",
"VertexTransitive", "WeaklyPerfect", "WeaklyRegular", "Web",
"WellCovered", "Wheel", "WhiteBishop", "Windmill", "Wreath",
"ZeroSymmetric", "ZeroTwo"}
And here's the labelling TriangularHoneycombAcuteKnight graph with 10 vertices (to take one of millions of examples).

And on and on and on and on....
