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.)

edited Dec 31 '18 at 19:24

the_fox

2,90021537

asked Dec 31 '18 at 18:13

1730

8911714

2

$begingroup$
Just generate the subsets of $E(K_n)$.
$endgroup$
– Chris Godsil
Dec 31 '18 at 19:10

$begingroup$
@ChrisGodsil Yep. No idea why I didn't think to do that. This question could probably be closed now.
$endgroup$
– 1730
Dec 31 '18 at 19:14

add a comment |

edited Dec 31 '18 at 19:24

the_fox

2,90021537

asked Dec 31 '18 at 18:13

1730

8911714

2

$begingroup$
Just generate the subsets of $E(K_n)$.
$endgroup$
– Chris Godsil
Dec 31 '18 at 19:10

$begingroup$
@ChrisGodsil Yep. No idea why I didn't think to do that. This question could probably be closed now.
$endgroup$
– 1730
Dec 31 '18 at 19:14

add a comment |

edited Dec 31 '18 at 19:24

the_fox

2,90021537

asked Dec 31 '18 at 18:13

1730

8911714

graph-theory

edited Dec 31 '18 at 19:24

the_fox

2,90021537

asked Dec 31 '18 at 18:13

1730

8911714

edited Dec 31 '18 at 19:24

the_fox

2,90021537

asked Dec 31 '18 at 18:13

1730

8911714

edited Dec 31 '18 at 19:24

the_fox

2,90021537

edited Dec 31 '18 at 19:24

the_fox

2,90021537

edited Dec 31 '18 at 19:24

the_fox

2,90021537

asked Dec 31 '18 at 18:13

1730

8911714

asked Dec 31 '18 at 18:13

1730

8911714

asked Dec 31 '18 at 18:13

1730

8911714

2

$begingroup$
Just generate the subsets of $E(K_n)$.
$endgroup$
– Chris Godsil
Dec 31 '18 at 19:10

$begingroup$
@ChrisGodsil Yep. No idea why I didn't think to do that. This question could probably be closed now.
$endgroup$
– 1730
Dec 31 '18 at 19:14

add a comment |

2

$begingroup$
Just generate the subsets of $E(K_n)$.
$endgroup$
– Chris Godsil
Dec 31 '18 at 19:10

$begingroup$
@ChrisGodsil Yep. No idea why I didn't think to do that. This question could probably be closed now.
$endgroup$
– 1730
Dec 31 '18 at 19:14

Just generate the subsets of $E(K_n)$.

– Chris Godsil
Dec 31 '18 at 19:10

@ChrisGodsil Yep. No idea why I didn't think to do that. This question could probably be closed now.

– 1730
Dec 31 '18 at 19:14

add a comment |

1 Answer
1

active

oldest

votes

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

enter image description here

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

enter image description here

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).

enter image description here

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

edited Dec 31 '18 at 20:12

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

$begingroup$
This is neither complete (for any interesting $n$) nor in any real sense a database of labeled graphs. (Or else it is a database of labeled graphs, but a far more incomplete one; e.g., it contains only one cycle graph on $n$ vertices out of all $frac{(n-1)!}{2}$ possibilities.)
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:18

$begingroup$
The figure was, of course, a subset of the graphs. Of course. And labelling is trivial. (I'll update the answer in a moment.)
$endgroup$
– David G. Stork
Dec 31 '18 at 19:22

$begingroup$
I am not speaking about the figure; the actual GraphData database is incomplete - intentially so, since it only focuses on "interesting" graphs.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:49

$begingroup$
You can generate any graph with $n$ vertexes.
$endgroup$
– David G. Stork
Dec 31 '18 at 19:52

$begingroup$
Yes, so the correct answer is Graph[Range[n], #] & /@ Subsets[UndirectedEdge @@@ Subsets[Range[n], {2}]]. The mention of GraphData is a red herring.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:53

|
show 2 more comments

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1 Answer
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active

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1 Answer
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oldest

votes

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

enter image description here

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

enter image description here

Here's just a list of the graph classes:

And here's the labelling TriangularHoneycombAcuteKnight graph with 10 vertices (to take one of millions of examples).

enter image description here

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

edited Dec 31 '18 at 20:12

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

$begingroup$
This is neither complete (for any interesting $n$) nor in any real sense a database of labeled graphs. (Or else it is a database of labeled graphs, but a far more incomplete one; e.g., it contains only one cycle graph on $n$ vertices out of all $frac{(n-1)!}{2}$ possibilities.)
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:18

$begingroup$
The figure was, of course, a subset of the graphs. Of course. And labelling is trivial. (I'll update the answer in a moment.)
$endgroup$
– David G. Stork
Dec 31 '18 at 19:22

$begingroup$
I am not speaking about the figure; the actual GraphData database is incomplete - intentially so, since it only focuses on "interesting" graphs.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:49

$begingroup$
You can generate any graph with $n$ vertexes.
$endgroup$
– David G. Stork
Dec 31 '18 at 19:52

$begingroup$
Yes, so the correct answer is Graph[Range[n], #] & /@ Subsets[UndirectedEdge @@@ Subsets[Range[n], {2}]]. The mention of GraphData is a red herring.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:53

|
show 2 more comments

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

enter image description here

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

enter image description here

Here's just a list of the graph classes:

And here's the labelling TriangularHoneycombAcuteKnight graph with 10 vertices (to take one of millions of examples).

enter image description here

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

edited Dec 31 '18 at 20:12

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

$begingroup$
This is neither complete (for any interesting $n$) nor in any real sense a database of labeled graphs. (Or else it is a database of labeled graphs, but a far more incomplete one; e.g., it contains only one cycle graph on $n$ vertices out of all $frac{(n-1)!}{2}$ possibilities.)
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:18

$begingroup$
The figure was, of course, a subset of the graphs. Of course. And labelling is trivial. (I'll update the answer in a moment.)
$endgroup$
– David G. Stork
Dec 31 '18 at 19:22

$begingroup$
I am not speaking about the figure; the actual GraphData database is incomplete - intentially so, since it only focuses on "interesting" graphs.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:49

$begingroup$
You can generate any graph with $n$ vertexes.
$endgroup$
– David G. Stork
Dec 31 '18 at 19:52

$begingroup$
Yes, so the correct answer is Graph[Range[n], #] & /@ Subsets[UndirectedEdge @@@ Subsets[Range[n], {2}]]. The mention of GraphData is a red herring.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:53

|
show 2 more comments

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

enter image description here

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

enter image description here

Here's just a list of the graph classes:

And here's the labelling TriangularHoneycombAcuteKnight graph with 10 vertices (to take one of millions of examples).

enter image description here

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

edited Dec 31 '18 at 20:12

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

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

enter image description here

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

enter image description here

Here's just a list of the graph classes:

And here's the labelling TriangularHoneycombAcuteKnight graph with 10 vertices (to take one of millions of examples).

enter image description here

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

edited Dec 31 '18 at 20:12

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

edited Dec 31 '18 at 20:12

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

answered Dec 31 '18 at 18:46

David G. Stork

11k41432

$begingroup$
This is neither complete (for any interesting $n$) nor in any real sense a database of labeled graphs. (Or else it is a database of labeled graphs, but a far more incomplete one; e.g., it contains only one cycle graph on $n$ vertices out of all $frac{(n-1)!}{2}$ possibilities.)
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:18

$begingroup$
The figure was, of course, a subset of the graphs. Of course. And labelling is trivial. (I'll update the answer in a moment.)
$endgroup$
– David G. Stork
Dec 31 '18 at 19:22

$begingroup$
I am not speaking about the figure; the actual GraphData database is incomplete - intentially so, since it only focuses on "interesting" graphs.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:49

$begingroup$
You can generate any graph with $n$ vertexes.
$endgroup$
– David G. Stork
Dec 31 '18 at 19:52

$begingroup$
Yes, so the correct answer is Graph[Range[n], #] & /@ Subsets[UndirectedEdge @@@ Subsets[Range[n], {2}]]. The mention of GraphData is a red herring.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:53

|
show 2 more comments

$begingroup$
This is neither complete (for any interesting $n$) nor in any real sense a database of labeled graphs. (Or else it is a database of labeled graphs, but a far more incomplete one; e.g., it contains only one cycle graph on $n$ vertices out of all $frac{(n-1)!}{2}$ possibilities.)
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:18

$begingroup$
The figure was, of course, a subset of the graphs. Of course. And labelling is trivial. (I'll update the answer in a moment.)
$endgroup$
– David G. Stork
Dec 31 '18 at 19:22

$begingroup$
I am not speaking about the figure; the actual GraphData database is incomplete - intentially so, since it only focuses on "interesting" graphs.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:49

$begingroup$
You can generate any graph with $n$ vertexes.
$endgroup$
– David G. Stork
Dec 31 '18 at 19:52

$begingroup$
Yes, so the correct answer is Graph[Range[n], #] & /@ Subsets[UndirectedEdge @@@ Subsets[Range[n], {2}]]. The mention of GraphData is a red herring.
$endgroup$
– Misha Lavrov
Dec 31 '18 at 19:53

This is neither complete (for any interesting $n$) nor in any real sense a database of labeled graphs. (Or else it is a database of labeled graphs, but a far more incomplete one; e.g., it contains only one cycle graph on $n$ vertices out of all $frac{(n-1)!}{2}$ possibilities.)

– Misha Lavrov
Dec 31 '18 at 19:18

The figure was, of course, a subset of the graphs. Of course. And labelling is trivial. (I'll update the answer in a moment.)

– David G. Stork
Dec 31 '18 at 19:22

I am not speaking about the figure; the actual GraphData database is incomplete - intentially so, since it only focuses on "interesting" graphs.

– Misha Lavrov
Dec 31 '18 at 19:49

You can generate any graph with $n$ vertexes.

– David G. Stork
Dec 31 '18 at 19:52

Yes, so the correct answer is Graph[Range[n], #] & /@ Subsets[UndirectedEdge @@@ Subsets[Range[n], {2}]]. The mention of GraphData is a red herring.

– Misha Lavrov
Dec 31 '18 at 19:53

|
show 2 more comments

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