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‎README.md‎

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# README #
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## digraphs-lib ##
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### Library of digraphs for the Digraphs package of GAP ###
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# README for digraphs-lib
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### Library of digraphs for the Digraphs package of GAP ###
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In this directory is a collection of various types of digraphs, which can be
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loaded into the GAP computational algebra system using the [Digraphs
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package](http://www-circa.mcs.st-and.ac.uk/~jamesm/digraphs.php). It is a
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package](https://gap-packages.github.io/Digraphs). It is a
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completely optional addition to the package, which can be used to produce
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examples of digraphs for use in the package.
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Getting digraphs-lib
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--------------------
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The latest version of this library is available at the following link:
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The latest version of this library is available at
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<http://gap-packages.github.io/Digraphs>.
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https://bitbucket.org/james-d-mitchell/digraphs/downloads
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Simply download it and extract the archive into the root directory of your
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Simply download the archive, and extract it into the root directory of your
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Digraphs installation. This should result in a `digraphs-lib` directory inside
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your `digraphs` directory.
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Using digraphs-lib
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------------------
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Once the library is installed, simply launch GAP, load the Digraphs package, and
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```
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gap> LoadPackage("digraphs", false);;
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gap> filename := "~/gap/pkg/digraphs/digraphs-lib/latin.g6.gz";;
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gap> filename := Concatenation(DIGRAPHS_Dir(), "/digraphs-lib/latin.g6.gz");;
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gap> latin_graphs := ReadDigraphs(filename);
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[ <digraph with 100 vertices, 2700 edges>,
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<digraph with 121 vertices, 3630 edges>,
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<digraph with 144 vertices, 4752 edges>,
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<digraph with 169 vertices, 6084 edges>,
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<digraph with 196 vertices, 7644 edges>,
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<digraph with 225 vertices, 9450 edges>,
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<digraph with 256 vertices, 11520 edges>,
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<digraph with 289 vertices, 13872 edges>,
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<digraph with 324 vertices, 16524 edges>,
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<digraph with 361 vertices, 19494 edges>,
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<digraph with 4 vertices, 12 edges>,
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<digraph with 400 vertices, 22800 edges>,
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<digraph with 441 vertices, 26460 edges>,
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<digraph with 484 vertices, 30492 edges>,
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<digraph with 529 vertices, 34914 edges>,
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<digraph with 576 vertices, 39744 edges>,
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<digraph with 625 vertices, 45000 edges>,
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<digraph with 676 vertices, 50700 edges>,
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<digraph with 729 vertices, 56862 edges>,
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<digraph with 784 vertices, 63504 edges>,
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<digraph with 841 vertices, 70644 edges>,
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<digraph with 9 vertices, 54 edges>,
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<digraph with 900 vertices, 78300 edges>,
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<digraph with 16 vertices, 144 edges>,
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<digraph with 25 vertices, 300 edges>,
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<digraph with 36 vertices, 540 edges>,
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<digraph with 49 vertices, 882 edges>,
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<digraph with 64 vertices, 1344 edges>,
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<digraph with 81 vertices, 1944 edges> ]
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[ <immutable digraph with 100 vertices, 2700 edges>,
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<immutable digraph with 121 vertices, 3630 edges>,
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<immutable digraph with 144 vertices, 4752 edges>,
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<immutable digraph with 169 vertices, 6084 edges>,
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<immutable digraph with 196 vertices, 7644 edges>,
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<immutable digraph with 225 vertices, 9450 edges>,
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<immutable digraph with 256 vertices, 11520 edges>,
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<immutable digraph with 289 vertices, 13872 edges>,
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<immutable digraph with 324 vertices, 16524 edges>,
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<immutable digraph with 361 vertices, 19494 edges>,
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<immutable digraph with 4 vertices, 12 edges>,
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<immutable digraph with 400 vertices, 22800 edges>,
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<immutable digraph with 441 vertices, 26460 edges>,
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<immutable digraph with 484 vertices, 30492 edges>,
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<immutable digraph with 529 vertices, 34914 edges>,
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<immutable digraph with 576 vertices, 39744 edges>,
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<immutable digraph with 625 vertices, 45000 edges>,
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<immutable digraph with 676 vertices, 50700 edges>,
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<immutable digraph with 729 vertices, 56862 edges>,
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<immutable digraph with 784 vertices, 63504 edges>,
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<immutable digraph with 841 vertices, 70644 edges>,
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<immutable digraph with 9 vertices, 54 edges>,
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<immutable digraph with 900 vertices, 78300 edges>,
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<immutable digraph with 16 vertices, 144 edges>,
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<immutable digraph with 25 vertices, 300 edges>,
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<immutable digraph with 36 vertices, 540 edges>,
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<immutable digraph with 49 vertices, 882 edges>,
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<immutable digraph with 64 vertices, 1344 edges>,
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<immutable digraph with 81 vertices, 1944 edges> ]
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```
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Types of digraph available
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--------------------------
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The following files were created by the authors of the Digraphs package:
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* `sparse.ds6.gz` - Sparse graphs (few edges per vertex)
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* `tournament.d6.gz` - Tournaments
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The following files contain symmetric graphs taken from the [nauty and Traces
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website](http://pallini.di.uniroma1.it/Graphs.html), by Brendan McKay and Adolfo
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Piperno:
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The following files contain symmetric digraphs (i.e. graphs) taken from the
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[nauty and Traces website](http://pallini.di.uniroma1.it/Graphs.html), by
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Brendan McKay and Adolfo Piperno:
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* `ag.s6.gz` - Affine geometry graphs
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* `cfi.s6.gz` - Cai, Fuerer and Immerman graphs
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* `sts-sw.g6.gz` - Steiner triple system graphs with switched edges
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* `triang.g6.gz` - Triangular graphs
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There are also some additional files containing graphs coming from finite geometry:
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* `fining.p.gz` - contains some graphs comining from finite geometries:
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(1): vertices are the generators of the hermitian polar space H(5,4), two vertices are adjacent iff they are skew
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(2): vertices are the generators of the hermitian quadrangle H(4,4), two vertices are adjacent iff they are skew
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(3): vertices areh the points and lines of the classical generalized quadrangle Q(4,8), two vertics are adjacent iff
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they are incident (and no loops!). This is a bipartite graph with diameter 4 and undirected girth 8
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(4): the bipartite graph (see (3)) of an elation generalized quadrangle. This one was constructed as a coset geometry.
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(5): the bipartite graph of the split Cayley hexagon of order 4, diameter is 6 and girth is 12.
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(6): the bipartite graph of the Ree-Tits generalized octagon! This one has diameter 8 and girth 16!
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There are also some additional files, added by Jan De Beule, which containing
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graphs that come from finite geometry, which were
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* `fining.p.gz` contains some graphs coming from finite geometries:
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1. The vertices are the generators of the hermitian polar space `H(5,4)`,
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two vertices are adjacent iff they are skew.
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2. The vertices are the generators of the hermitian quadrangle `H(4,4)`, two
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vertices are adjacent iff they are skew.
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3. The vertices are the points and lines of the classical generalised
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quadrangle `Q(4,8)`, two vertices are adjacent iff they are distinct and
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incident (no loops!). This is a bipartite graph with diameter 4 and
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undirected girth 8.
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4. The bipartite graph (see (3)) of an elation generalised quadrangle. This
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one was constructed as a coset geometry.
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5. The bipartite graph of the split Cayley hexagon of order 4, the diameter
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is 6 and the girth is 12.
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6. The bipartite graph of the Ree-Tits generalised octagon. This has
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diameter 8 and girth 16!
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* `polar_graphs.p.gz` A polar graph is by definition the point graph of a
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finite classical polar space. Note that such a geometry is a partial linear
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space, so not every pair of points is a pair of collinear points. Two
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points are adjacent iff they differe and they are collinear. The diamter of
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these graphs is 2, their undirected girth 3, the latter since these spaces
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contain lines. Reading in this file requires around 4 Gb.
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* `dual_polar_graphs.p.gz` We consider again finite classical polar
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spaces. Such geometries contain points, lines, etc., up to maximal
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subspaces, which all have the same projective dimension. The vertices of a
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dual polar graph are these maximal subspaces, of dimension d say, and they
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are adjacent iff they differ and meet in a d-1 dimensional projective
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subspace. Reading in this file requres around 5Gb.
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finite classical polar space. Note that such a geometry is a partial linear
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space, so not every pair of points is a pair of collinear points. Two points
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are adjacent iff they are distinct and collinear. The diameter of these
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graphs is 2, their undirected girth 3, the latter since these spaces contain
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lines. Reading in this file requires around 4 Gb of memory.
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* `dual_polar_graphs.p.gz` We consider again finite classical polar spaces.
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Such geometries contain points, lines, etc., up to maximal subspaces, which
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all have the same projective dimension. The vertices of a dual polar graph
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are these maximal subspaces, of dimension, say, `d`, and they are adjacent
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iff they are distinct and meet in a `d-1` dimensional projective subspace.
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Reading in this file requires around 5 Gb of memory.
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* `generators_graphs.p.gz` (parts 1, 2 and 3). We consider again finite
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classical polar spaces. The vertices are the maximal subspaces and they
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are adjacent iff they differ and are skew. Reading part 2 requires almost
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6Gb, reading part 3 requires again 6Gb. Reading part 1 requires much less
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(around 1.5Gb).
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* `generators_graphs.p.gz` (Parts 1, 2, and 3). We again consider finite
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classical polar spaces. The vertices are the maximal subspaces and they are
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adjacent iff they are distinct and skew. Reading part 2 requires almost 6 Gb
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of memory, and reading part 3 requires another 6 Gb. Reading part 1 requires
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much less memory, around 1.5 Gb.
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* `incidence_graphs.p.gz` a generalized polygon of gonality n is a point line
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geometry, such that if one considers the incidence graph, i.e. the
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vertices are the points and the lines, adjacency is incidence (withouth
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loops), then it has diameter n and girth 2n. All graphs in this repository
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are incidence graphs of generalized polygons. Note that by a famous
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theorem, thick GPs (i.e. at least three points on a line and dually, at
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least three lines on a point), have gonality 3,4,6 or 8. The repository
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contains the incidence graph of the smallest generalized octogon, some
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generalized hexagons, and a lot of generalized quadrangles, and some
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projective planes. To read it completely, around 1.5Gb is requiered.
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which were added by Jan De Beule.
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* `incidence_graphs.p.gz` A generalised polygon of gonality n is a point line
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geometry, such that if one considers the incidence graph, i.e. the vertices
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are the points and adjacency is incidence (without loops), then it has
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diameter n and girth 2n. All graphs in this file are incidence graphs of
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generalised polygons. Note that by a famous theorem, thick GPs (i.e. at
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least three points on a line and dually, at least three lines on a point),
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have gonality 3, 4, 6, or 8. This file contains the incidence graph of the
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smallest generalised octogon, some generalised hexagons, and a lot of
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generalised quadrangles, and some projective planes. To read it completely,
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around 1.5 Gb of memory is required.

‎extreme.d6‎

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