#############################################################################
##
#W io.xml
#Y Copyright (C) 2014-17 James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
<#GAPDoc Label="IteratorFromDigraphFile">
<ManSection>
<Func Name="IteratorFromDigraphFile" Arg="filename [, decoder]"/>
<Returns>An iterator.</Returns>
<Description>
If <A>filename</A> is a string representing the name of a file containing
encoded digraphs, then <C>IteratorFromDigraphFile</C> returns an iterator
for which the value of <Ref Oper="NextIterator" BookName="ref"/> is the
next digraph encoded in the file.
<P/>
If the optional argument <A>decoder</A> is specified and is a function
which decodes a string into a digraph, then <C>IteratorFromDigraphFile</C>
will use <A>decoder</A> to decode the digraphs contained in <A>filename</A>.
<P/>
The purpose of this function is to easily allow looping over digraphs
encoded in a file when loading all of the encoded digraphs would require
too much memory. <P/>
To see what file types are available, see <Ref Func="WriteDigraphs"/>.
<Example><![CDATA[
gap> filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/man.d6.gz");;
gap> file := DigraphFile(filename, "w");;
gap> for i in [1 .. 10] do
> WriteDigraphs(file, Digraph([[1, 3], [2], [1, 2]]));
> od;
gap> IO_Close(file);;
gap> iter := IteratorFromDigraphFile(filename);
<iterator>
gap> for x in iter do od;
]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="DigraphFile">
<ManSection>
<Func Name="DigraphFile" Arg="filename [, coder][, mode]"/>
<Returns>An IO file object.</Returns>
<Description>
If <A>filename</A> is a string representing the name of a file, then
<C>DigraphFile</C> returns an &IO; package file object for that file.
<P/>
If the optional argument <A>coder</A> is specified
and is a function which either encodes a digraph as a string, or decodes a
string into a digraph, then this function will be used when reading or
writing to the returned file object. If the optional argument <A>coder</A>
is not specified, then the encoding of the digraphs in the returned file
object must be specified in the the file extension. The file extension must
be one of: <C>.g6</C>, <C>.s6</C>, <C>.d6</C>, <C>.ds6</C>, <C>.txt</C>,
<C>.p</C>, or <C>.pickle</C>; more details of these file formats is given
below. <P/>
If the optional argument <A>mode</A> is specified, then it must be one of:
<C>"w"</C> (for write), <C>"a"</C> (for append), or <C>"r"</C> (for read).
If <A>mode</A> is not specified, then <C>"r"</C> is used by default. <P/>
If <A>filename</A> ends in one of: <C>.gz</C>, <C>.bz2</C>, or
<C>.xz</C>, then the digraphs which are read from, or written to, the
returned file object are decompressed, or compressed, appropriately.
<P/>
The file object returned by <C>DigraphFile</C> can be given as the first
argument for either of the functions <Ref Func="ReadDigraphs"/> or <Ref
Func="WriteDigraphs"/>. The purpose of this is to reduce the overhead of
recreating the file object inside the functions <Ref Func="ReadDigraphs"/>
or <Ref Func="WriteDigraphs"/> when, for example, reading or writing many
digraphs in a loop.
<P/>
The currently supported file formats, and associated filename extensions,
are:
<List>
<Mark>graph6 (.g6)</Mark>
<Item>
A standard and widely-used format for undirected graphs, with no support
for loops or multiple edges. Only symmetric graphs are allowed -- each
edge is combined with its converse edge to produce a single undirected
edge. This format is best used for "dense" graphs -- those with many
edges per vertex.
</Item>
<Mark>sparse6 (.s6)</Mark>
<Item>
Unlike graph6, sparse6 has support for loops and multiple edges.
However, its use is still limited to symmetric graphs. This format is
better-suited to "sparse" graphs -- those with few edges per vertex.
</Item>
<Mark>digraph6 (.d6)</Mark>
<Item>
This format is based on graph6, but stores direction information -
therefore is not limited to symmetric graphs. Loops are allowed, but
multiple edges are not. Best compression with "dense" graphs.
</Item>
<Mark>disparse6 (.ds6)</Mark>
<Item>
Any type of digraph can be encoded in disparse6: directions, loops, and
multiple edges are all allowed. Similar to sparse6, this has the best
compression rate with "sparse" graphs.
</Item>
<Mark>plain text (.txt)</Mark>
<Item>
This is a human-readable format which stores graphs in the form
<C>0 7 0 8 1 7 2 8 3 8 4 8 5 8 6 8</C> i.e. pairs of vertices
describing edges in a graph. More specifically, the vertices making up
one edge must be separated by a single space, and pairs of vertices must
be separated by two spaces. <P/>
See <Ref Oper="ReadPlainTextDigraph"/> for a more flexible way to store
digraphs in a plain text file. <P/>
</Item>
<Mark>pickled (<F>.p</F> or <F>.pickle</F>)</Mark>
<Item>
Digraphs are pickled using the &IO; package. This is particularly good
when the <Ref Attr="DigraphGroup"/> is non-trivial.
</Item>
<Mark>dreadnaut (.dre)</Mark>
<Item>
A graph format designed for directed and undirected graphs.
The format supports loops but multiple edges are ignored. The format consists of an
initial section that defines the graph's structural properties, such as the number of
vertices, the starting value for vertices, and whether the graph is directed. This is followed
by a list of edges. For more information and examples of the format see
<URL Text="nauty and Traces User's Guide">http://pallini.di.uniroma1.it/Guide.html</URL>.<P/>
</Item>
<Mark> DIMACS (.dimacs) </Mark>
<Item>
A graph format that can be used for symmetric digraphs. For a more detailed description, see <Ref Oper="WriteDIMACSDigraph"/>
</Item>
</List>
<#GAPDoc Label="String">
<ManSection>
<Attr Name="String" Arg="digraph"/>
<Oper Name="PrintString" Arg="digraph"/>
<Returns>A string.</Returns>
<Description>
Returns a string <C>string</C> such that <C>EvalString(string)</C>
is equal to <A>digraph</A>, and has the same mutability.
See <Ref Func="EvalString" BookName="ref" />.
<P/>
The methods installed for <C>String</C> make some attempts to
ensure that <C>string</C> has as short a length as possible, but
there may exist shorter strings that also evaluate to <A>digraph</A>.
<P/>
It is possible that <C>string</C> may contain escaped special
characters. To obtain a representation of <A>digraph</A> that
can be entered as GAP input, please use
<Ref Func="Print" BookName="ref" />.
Note that <C>Print</C> for a digraph delegates to
<C>PrintString</C>, which delegates to <C>String</C>.
<Log><![CDATA[
gap> D := CycleDigraph(3);
<immutable cycle digraph with 3 vertices>
gap> Print(D);
CycleDigraph(3);
gap> G := PetersenGraph(IsMutableDigraph);
<mutable digraph with 10 vertices, 30 edges>
gap> String(G); "DigraphFromGraph6String(IsMutableDigraph, \"IheA@GUAo\");"
gap> Print(last);
DigraphFromGraph6String(IsMutableDigraph, "IheA@GUAo");
gap> DigraphFromGraph6String(IsMutableDigraph, "IheA@GUAo");
<mutable digraph with 10 vertices, 30 edges>
]]></Log>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="DigraphFromGraph6String">
<ManSection>
<Oper Name="DigraphFromGraph6String" Arg="[filt, ]str"/>
<Oper Name="DigraphFromDigraph6String" Arg="[filt, ]str"/>
<Oper Name="DigraphFromSparse6String" Arg="[filt, ]str"/>
<Oper Name="DigraphFromDiSparse6String" Arg="[filt, ]str"/>
<Returns>A digraph.</Returns>
<Description>
If <A>str</A> is a string encoding a graph in Graph6, Digraph6, Sparse6 or
DiSparse6 format, then the corresponding function returns a digraph. In the
case of either Graph6 or Sparse6, formats which do not support directed
edges, this will be a digraph such that for every edge, the edge going in
the opposite direction is also present.<P/>
Each of these functions takes an optional first argument <A>filt</A>,
which should be either <Ref Filt="IsMutableDigraph"/>
or <Ref Filt="IsImmutableDigraph"/>,
and which specifies whether the output digraph shall
be mutable or immutable.
If no first argument is provided, then an immutable
digraph is returned by default.
<Example><![CDATA[
gap> DigraphFromGraph6String("?");
<immutable empty digraph with 0 vertices>
gap> DigraphFromGraph6String("C]");
<immutable symmetric digraph with 4 vertices, 8 edges>
gap> DigraphFromGraph6String("H?AAEM{");
<immutable symmetric digraph with 9 vertices, 22 edges>
gap> DigraphFromDigraph6String("&?");
<immutable empty digraph with 0 vertices>
gap> DigraphFromDigraph6String(IsMutableDigraph, "&DOOOW?");
<mutable digraph with 5 vertices, 5 edges>
gap> DigraphFromDigraph6String("&CQFG");
<immutable digraph with 4 vertices, 6 edges>
gap> DigraphFromDigraph6String("&IM[SrKLc~lhesbU[F_");
<immutable digraph with 10 vertices, 51 edges>
gap> DigraphFromDiSparse6String(".CaWBGA?b");
<immutable multidigraph with 4 vertices, 9 edges>
]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="ReadDigraphs">
<ManSection>
<Func Name="ReadDigraphs" Arg="filename[, decoder][, n]"/>
<Returns>A digraph, or a list of digraphs.</Returns>
<Description>
If <A>filename</A> is a string containing the name of a file containing
encoded digraphs or an &IO; file object created using <Ref
Func="DigraphFile"/>, then <C>ReadDigraphs</C> returns the digraphs
encoded in the file as a list. Note that if <A>filename</A> is a
compressed file, which has been compressed appropriately to give a filename
extension of <C>.gz</C>, <C>.bz2</C>, or <C>.xz</C>, then
<C>ReadDigraphs</C> can read <A>filename</A> without it first needing to be
decompressed.
<P/>
If the optional argument <A>decoder</A> is specified
and is a function which decodes a string into a digraph,
then <C>ReadDigraphs</C> will use <A>decoder</A> to decode the digraphs
contained in <A>filename</A>.<P/>
If the optional argument <A>n</A> is specified, then <C>ReadDigraphs</C>
returns the <A>n</A>th digraph encoded in the file <A>filename</A>.
<P/>
If the optional argument <A>decoder</A> is not specified, then
<C>ReadDigraphs</C> will deduce which decoder to use based on the filename
extension of <A>filename</A> (after removing the compression-related
filename extensions <C>.gz</C>, <C>.bz2</C>, and <C>.xz</C>). For example,
if the filename extension is <C>.g6</C>, then <C>ReadDigraphs</C> will use
the graph6 decoder <Ref Oper="DigraphFromGraph6String"/>.
<P/>
The currently supported file formats, and associated filename extensions,
are:
<List>
<Mark>graph6 (.g6)</Mark>
<Item>
A standard and widely-used format for undirected graphs, with no support
for loops or multiple edges. Only symmetric graphs are allowed -- each
edge is combined with its converse edge to produce a single undirected
edge. This format is best used for "dense" graphs -- those with many
edges per vertex.
</Item>
<Mark>sparse6 (.s6)</Mark>
<Item>
Unlike graph6, sparse6 has support for loops and multiple edges.
However, its use is still limited to symmetric graphs. This format is
better-suited to "sparse" graphs -- those with few edges per vertex.
</Item>
<Mark>digraph6 (.d6)</Mark>
<Item>
This format is based on graph6, but stores direction information -
therefore is not limited to symmetric graphs. Loops are allowed, but
multiple edges are not. Best compression with "dense" graphs.
</Item>
<Mark>disparse6 (.ds6)</Mark>
<Item>
Any type of digraph can be encoded in disparse6: directions, loops, and
multiple edges are all allowed. Similar to sparse6, this has the best
compression rate with "sparse" graphs.
</Item>
<Mark>plain text (.txt)</Mark>
<Item>
This is a human-readable format which stores graphs in the form
<C>0 7 0 8 1 7 2 8 3 8 4 8 5 8 6 8</C> i.e. pairs of vertices
describing edges in a graph. More specifically, the vertices making up
one edge must be separated by a single space, and pairs of vertices must
be separated by two spaces. <P/>
See <Ref Oper="ReadPlainTextDigraph"/> for a more flexible way to store
digraphs in a plain text file. <P/> <!-- Just so I remember: <C>ReadPlainTextDigraph("data-local/soc-Epinions1.txt.gz", "\t", 1, '#');</C>
-->
</Item>
<Mark>pickled (<F>.p</F> or <F>.pickle</F>)</Mark>
<Item>
Digraphs are pickled using the &IO; package. This is particularly good
when the <Ref Attr="DigraphGroup"/> is non-trivial. <P/>
</Item>
<Mark>dreadnaut (.dre)</Mark>
<Item>
A graph format designed for directed and undirected graphs.
The format supports loops but multiple edges are ignored. The format consists of an
initial section that defines the graph's structural properties, such as the number of
vertices, the starting value for vertices, and whether the graph is directed. This is followed
by a list of edges. For more information and examples of the format see
<URL Text="nauty and Traces User's Guide">http://pallini.di.uniroma1.it/Guide.html</URL>. <P/>
</Item>
<Mark> DIMACS (.dimacs) </Mark>
<Item>
A graph format that can be used for symmetric digraphs. For a more detailed description, see <Ref Oper="WriteDIMACSDigraph"/>
</Item>
</List>
<Example><![CDATA[
gap> ReadDigraphs(
> Concatenation(DIGRAPHS_Dir(), "/data/graph5.g6.gz"), 10);
<immutable symmetric digraph with 5 vertices, 8 edges>
gap> ReadDigraphs(
> Concatenation(DIGRAPHS_Dir(), "/data/graph5.g6.gz"), 17);
<immutable symmetric digraph with 5 vertices, 12 edges>
gap> ReadDigraphs(
> Concatenation(DIGRAPHS_Dir(), "/data/tree9.4.txt"));
[ <immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges>,
<immutable digraph with 9 vertices, 8 edges> ]]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="WriteDigraphs">
<ManSection>
<Func Name="WriteDigraphs" Arg="filename, digraphs[, encoder] [, mode]"/>
<Description>
If <A>digraphs</A> is a list of digraphs or a digraph and <A>filename</A>
is a string or an &IO; file object created using <Ref Func="DigraphFile"/>,
then <C>WriteDigraphs</C> writes the digraphs to the file represented by
<A>filename</A>. If the supplied filename ends in one of the extensions
<C>.gz</C>, <C>.bz2</C>, or <C>.xz</C>, then the file will be compressed
appropriately. Excluding these extensions, if the file ends with an
extension in the list below, the corresponding graph format will be used to
encode it. If such an extension is not included, an appropriate format
will be chosen intelligently, and an extension appended, to minimise file
size.
<P/>
<!-- TODO: encode and mode. -->
For more verbose information on the progress of the function, set the info
level of <A>InfoDigraphs</A> to 1 or higher, using <C>SetInfoLevel</C>.<P/>
The currently supported file formats are:
<List>
<Mark>graph6 (.g6)</Mark>
<Item>
A standard and widely-used format for undirected graphs, with no support
for loops or multiple edges. Only symmetric graphs are allowed -- each
edge is combined with its converse edge to produce a single undirected
edge. This format is best used for "dense" graphs -- those with many
edges per vertex.
</Item>
<Mark>sparse6 (.s6)</Mark>
<Item>
Unlike graph6, sparse6 has support for loops and multiple edges.
However, its use is still limited to symmetric graphs. This format is
better-suited to "sparse" graphs -- those with few edges per vertex.
</Item>
<Mark>digraph6 (.d6)</Mark>
<Item>
This format is based on graph6, but stores direction information -
therefore is not limited to symmetric graphs. Loops are allowed, but
multiple edges are not. Best compression with "dense" graphs.
</Item>
<Mark>disparse6 (.ds6)</Mark>
<Item>
Any type of digraph can be encoded in disparse6: directions, loops, and
multiple edges are all allowed. Similar to sparse6, this has the best
compression rate with "sparse" graphs.
</Item>
<Mark>plain text (.txt)</Mark>
<Item>
This is a human-readable format which stores graphs in the form
<C>0 7 0 8 1 7 2 8 3 8 4 8 5 8 6 8</C> i.e. pairs of vertices
describing edges in a graph. More specifically, the vertices making up
one edge must be separated by a single space, and pairs of vertices must
be separated by two spaces. <P/>
See <Ref Oper="ReadPlainTextDigraph"/> for a more flexible way to store
digraphs in a plain text file. <P/> <!-- Just so I remember: <C>ReadPlainTextDigraph("data-local/soc-Epinions1.txt.gz", "\t", 1, '#');</C>
-->
</Item>
<Mark>pickled (<F>.p</F> or <F>.pickle</F>)</Mark>
<Item>
Digraphs are pickled using the &IO; package. This is particularly good
when the <Ref Attr="DigraphGroup"/> is non-trivial.
</Item>
<Mark>dreadnaut (.dre)</Mark>
<Item>
A graph format designed for directed and undirected graphs.
The format supports loops but multiple edges are ignored. The format consists of an
initial section that defines the graph's structural properties, such as the number of
vertices, the starting value for vertices, and whether the graph is directed. This is followed
by a list of edges. For more information and examples of the format see
<URL Text="nauty and Traces User's Guide">http://pallini.di.uniroma1.it/Guide.html</URL>. <P/>
</Item>
<Mark> DIMACS (.dimacs) </Mark>
<Item>
A graph format that can be used for symmetric digraphs. For a more detailed description, see <Ref Oper="WriteDIMACSDigraph"/>
</Item>
</List>
<#GAPDoc Label="Graph6String">
<ManSection>
<Oper Name="Graph6String" Arg="digraph"/>
<Oper Name="Digraph6String" Arg="digraph"/>
<Oper Name="Sparse6String" Arg="digraph"/>
<Oper Name="DiSparse6String" Arg="digraph"/>
<Returns>A string.</Returns>
<Description>
These four functions return a highly compressed string fully describing the
digraph <A>digraph</A>. <P/>
Graph6 and Digraph6 are formats best used on small, dense graphs, if
applicable. For larger, sparse graphs use <E>Sparse6</E> and
<E>Disparse6</E> (this latter also preserves multiple edges). <P/>
See <Ref Func="WriteDigraphs"/>.
<Example><![CDATA[
gap> gr := Digraph([[2, 3], [1], [1]]);
<immutable digraph with 3 vertices, 4 edges>
gap> Sparse6String(gr); ":Bc"
gap> DiSparse6String(gr); ".Bc{f"
]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="DigraphPlainTextLineEncoder">
<ManSection>
<Func Name="DigraphPlainTextLineEncoder" Arg="delimiter1, [delimiter2,] offset"/>
<Oper Name="DigraphPlainTextLineDecoder" Arg="delimiter1, [delimiter2,] offset"/>
<Returns>A string.</Returns>
<Description>
These two functions return a function which encodes or decodes a digraph in
a plain text format.<P/>
<A>DigraphPlainTextLineEncoder</A> returns a function which takes a single
digraph as an argument. The function returns a string describing the edges
of that digraph; each edge is written as a pair of integers separated by the
string <A>delimiter2</A>, and the edges themselves are separated by the
string <A>delimiter1</A>. <A>DigraphPlainTextLineDecoder</A> returns the
corresponding decoder function, which takes a string argument in this format
and returns a digraph.<P/>
If only one delimiter is passed as an argument to
<A>DigraphPlainTextLineDecoder</A>, it will return a function which decodes
a single edge, returning its contents as a list of integers.<P/>
The argument <A>offset</A> should be an integer, which will describe a
number to be added to each vertex before it is encoded, or after it is
decoded. This may be used, for example, to label vertices starting at 0
instead of 1.<P/>
Note that the number of vertices of a digraph is not stored, and so vertices
which are not connected to any edge may be lost.
<#GAPDoc Label="PlainTextString">
<ManSection>
<Oper Name="PlainTextString" Arg="digraph"/>
<Oper Name="DigraphFromPlainTextString" Arg="s"/>
<Returns>A string.</Returns>
<Description>
<A>PlainTextString</A> takes a single digraph, and returns a string
describing the edges of that digraph. <A>DigraphFromPlainTextString</A>
takes such a string and returns the digraph which it describes. Each edge
is written as a pair of integers separated by a single space. The edges
themselves are separated by a double space. Vertex numbers are reduced by
1 when they are encoded, so that vertices in the string are labelled
starting at 0.<P/>
Note that the number of vertices of a digraph is not stored, and so vertices
which are not connected to any edge may be lost.<P/>
The operation <C>DigraphFromPlainTextString</C>
takes an optional first argument <Ref Filt="IsMutableDigraph"/>
or <Ref Filt="IsImmutableDigraph"/>, which specifies whether the output digraph shall
be mutable or immutable. If no first argument is provided, then an immutable
digraph is returned by default.
<#GAPDoc Label="WritePlainTextDigraph">
<ManSection>
<Func Name="WritePlainTextDigraph" Arg="filename, digraph, delimiter, offset"/>
<Oper Name="ReadPlainTextDigraph" Arg="filename, delimiter, offset, ignore"/>
<Description>
These functions write and read a single digraph in a human-readable plain
text format as follows: each line contains a single edge, and each edge is
written as a pair of integers separated by the string <A>delimiter</A>.<P/>
<A>filename</A> should be the name of a file which will be written to or
read from, and <A>offset</A> should be an integer which is added to each
vertex number as it is written or read. For example, if
<C>WritePlainTextDigraph</C> is called with <A>offset</A> <C>-1</C>, then
the vertices will be numbered in the file starting from 0 instead of 1 -
<C>ReadPlainTextDigraph</C> would then need to be called with <A>offset</A>
<C>1</C> to convert back to the original graph.<P/>
<A>ignore</A> should be a list of characters which will be ignored when
reading the graph.
<Example><![CDATA[
gap> gr := Digraph([[1, 2, 3], [1, 1], [2]]);
<immutable multidigraph with 3 vertices, 6 edges>
gap> filename := Concatenation(DIGRAPHS_Dir(), "/tst/out/plain.txt");;
gap> WritePlainTextDigraph(filename, gr, ",", -1);
gap> ReadPlainTextDigraph(filename, ",", 1, ['/', '%']);
<immutable multidigraph with 3 vertices, 6 edges>
]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="WriteDIMACSDigraph">
<ManSection>
<Oper Name="WriteDIMACSDigraph" Arg="filename, digraph"/>
<Oper Name="ReadDIMACSDigraph" Arg="filename"/>
<Description>
These operations write or read the single symmetric digraph <A>digraph</A>
to or from a file in DIMACS format, as appropriate. The operation
<C>WriteDIMACSDigraph</C> records the vertices and edges of <A>digraph</A>.
The vertex labels of <A>digraph</A> will be recorded only if they are
integers. See <Ref Prop="IsSymmetricDigraph"/> and <Ref
Oper="DigraphVertexLabels"/>.<P/>
The first argument <A>filename</A> should be the name of the file which will
be written to or read from. A file can contain one symmetric digraph in
DIMACS format. If <A>filename</A> ends in one of <C>.gz</C>, <C>.bz2</C>,
or <C>.xz</C>, then the file is compressed, or decompressed, appropriately.
<P/>
The DIMACS format is described as follows. Each line in the DIMACS file has
one of four types:
<List>
<Item>
A line beginning with <C>c</C> and followed by any number of characters
is a comment line, and is ignored.
</Item>
<Item>
A line beginning with <C>p</C> defines the numbers of vertices and edges
the digraph. This line has the format <C>p edge <nr_vertices>
<nr_edges></C>, where <C><nr_vertices></C> and
<C><nr_edges></C> are replaced by the relevant integers. There
must be exactly one such line in the file, and it must occur before any
of the following kinds of line.<P/>
Although it is required to be present, the value of
<C><nr_edges></C> will be ignored. The correct number of edges
will be deduced from the rest of the information in the file.
</Item>
<Item>
A line of the form <C>e <v> <w></C>, where <C><v></C>
and <C><w></C> are integers in the range <C>[1 ..
<nr_vertices>]</C>, specifies that there is a (symmetric) edge
in the digraph between the vertices <C><v></C> and
<C><w></C>. A symmetric edge only needs to be defined once; an
additional line <C>e <v> <w></C>, or <C>e <w>
<v></C>, will be interpreted as an additional, multiple, edge.
Loops are permitted.
</Item>
<Item>
A line of the form <C>n <v> <label></C>, where
<C><v></C> is an integer in the range <C>[1 ..
<nr_vertices>]</C> and <C><label></C> is an integer,
signifies that the vertex <C><v></C> has the label
<C><label></C> in the digraph. If a label is not specified for a
vertex, then <C>ReadDIMACSDigraph</C> will assign the label
<C>1</C>, according to the DIMACS specification.
</Item>
</List>
A detailed definition of the DIMACS format can be found in
<Ref Text="Appendix" Appendix="DIMACS"/> <Ref Appendix="DIMACS"/>.
<P/>
<#GAPDoc Label="TournamentLineDecoder">
<ManSection>
<Oper Name="TournamentLineDecoder" Arg="str"/>
<Returns>A digraph.</Returns>
<Description>
This function takes a string <A>str</A>, decodes it, and then returns the
tournament [see <Ref Prop="IsTournament"/>] which it defines, according to
the following rules. <P/>
The characters of the string <A>str</A> represent the entries in the upper
triangle of a tournament's adjacency matrix. The number of vertices
<C>n</C> will be detected from the length of the string and will be as
large as possible. <P/>
The first character represents the possible edge <C>1 -> 2</C>, the second
represents <C>1 -> 3</C> and so on until <C>1 -> n</C>; then the following
character represents <C>2 -> 3</C>, and so on up to the character which
represents the edge <C>n-1 -> n</C>. <P/>
If a character of the string with corresponding edge <C>i -> j</C> is equal
to <C>1</C>, then the edge <C>i -> j</C> is present in the tournament.
Otherwise, the edge <C>i -> j</C> is present instead. In this way, all the
possible edges are encoded one-by-one.
<#GAPDoc Label="AdjacencyMatrixUpperTriangleLineDecoder">
<ManSection>
<Oper Name="AdjacencyMatrixUpperTriangleLineDecoder" Arg="str"/>
<Returns>A digraph.</Returns>
<Description>
This function takes a string <A>str</A>, decodes it, and then returns the
topologically sorted digraph [see <Ref Attr="DigraphTopologicalSort"/>]
which it defines, according to the following rules. <P/>
The characters of the string <A>str</A> represent the entries in the upper
triangle of a digraph's adjacency matrix. The number of vertices n
will be detected from the length of the string and will be as large as
possible. <P/>
The first character represents the possible edge <C>1 -> 2</C>, the second
represents <C>1 -> 3</C> and so on until <C>1 -> n</C>; then the following
character represents <C>2 -> 3</C>, and so on up to the character which
represents the edge <C>n-1 -> n</C>. If a character of the string with
corresponding edge <C>i -> j</C> is equal to <C>1</C>, then this edge is
present in the digraph. Otherwise, it is not present. In this way, all the
possible edges are encoded one-by-one. <P/>
In particular, note that there exists no edge <C>[i, j]</C> if <M>j \leq
i</M>. In order words, the digraph will be topologically sorted.
<#GAPDoc Label="TCodeDecoder">
<ManSection>
<Oper Name="TCodeDecoder" Arg="str"/>
<Returns>A digraph.</Returns>
<Description>
If <A>str</A> is a string consisting of at least two non-negative integers
separated by spaces, then this function will attempt to return the digraph
which it defines as a TCode string. <P/>
The first integer of the string defines the number of vertices <C>v</C> in
the digraph, and the second defines the number of edges <C>e</C>. The
following <C>2e</C> integers should be vertex numbers in the range <C>[0 ..
v-1]</C>. These integers are read in pairs and define the digraph's
edges. This function will return an error if <A>str</A> has fewer than
<C>2e+2</C> entries. <P/>
Note that the vertex numbers will be incremented by 1 in the digraph
returned. Hence the string fragment <C>0 6</C> will describe the edge
<C>[1,7]</C>.
<Example><![CDATA[
gap> gr := TCodeDecoder("3 2 0 2 2 1");
<immutable digraph with 3 vertices, 2 edges>
gap> OutNeighbours(gr);
[ [ 3 ], [ ], [ 2 ] ]
gap> gr := TCodeDecoder("12 3 0 10 5 2 8 8");
<immutable digraph with 12 vertices, 3 edges>
gap> OutNeighbours(gr);
[ [ 11 ], [ ], [ ], [ ], [ ], [ 3 ], [ ], [ ], [ 9 ], [ ],
[ ], [ ] ]
]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="DigraphFromDreadnautString">
<ManSection>
<Oper Name="DigraphFromDreadnautString" Arg="s"/>
<Oper Name="DreadnautString" Arg="digraph[, partition]"/>
<Description>
These operations read or write a single digraph to or from a string in the dreadnaut format, as appropriate. <P/>
<C>DigraphFromDreadnautString</C> expects the argument <A>s</A> to be a string, containing a single graph in dreadnaut format,
and returns a digraph.<P/>
If the vertices are not already 1-indexed, their labels will be reindexed by subtracting a constant offset so that the smallest
label becomes 1, with the relative ordering of vertex labels being preserved.
If a partition is explicitly specified, each vertex will be assigned a label corresponding to its part in the partition.
Should the graph be undirected, the symmetric closure of the graph will be returned.
See <Ref Oper="DigraphVertexLabels"/> and <Ref Prop="DigraphSymmetricClosure"/>.<P/>
<C>DreadnautString</C> expects a digraph <A>digraph</A> and returns a string in dreadnaut format.
An optional second argument <A>partition</A> may be provided, which should be a list of length equal
to the number of vertices in <A>digraph</A>.
Each entry in the list assigns the corresponding vertex to a group, allowing you to specify a vertex partition.
For example, if the digraph has three vertices and <A>partition</A> is <C>["a", "b", "a"]</C>, this would
mean that the first and third vertices belong to the same part, and the second vertex belongs to a separate part.
This partition will appear in the resulting string as a line of the form <C>f = [...]</C>.<P/>
Note that <Ref Func="WriteDigraphs"/> does not support specifying a partition when writing a digraph to a file in dreadnaut format.
To include a partition when writing to a file, use <C>DreadnautString</C> to generate the string, then write it to a file using standard I/O functions.
If <A>digraph</A> has multiple edges, then <C>DreadnautString</C> returns a digraph constructed from <A>digraph</A> by removing all multiple edges.<P/>
A detailed description of commands and options in dreadnaut format can be found at
<URL Text="nauty and Traces User's Guide">http://pallini.di.uniroma1.it/Guide.html</URL>.
Of those commands, the following are supported: <C>n</C>, <C>g</C> (and all available subcommands),
<C>_</C> (underscore), <C>__</C> (double underscore), <C>f</C>, <C>$=#</C>, <C>$$</C>, <C>d, -d</C>, <C>"...", !</C>
<Example><![CDATA[
gap> gr := Digraph([[2], [1, 3, 4], [2, 4], [2, 3]]);
<immutable digraph with 4 vertices, 8 edges>
gap> s := DreadnautString(gr);;
gap> DigraphFromDreadnautString(s) = gr;
true
gap> DreadnautString(gr, ["a", "b", "b", "a"]); "n=4 $=1 d g\n1 : 2;\n2 : 1 3 4;\n3 : 2 4;\n4 : 2 3.\nf = [1 4 | 2 3]"]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="WholeFileEncoders">
<ManSection>
<Var Name="WholeFileEncoders"/>
<Var Name="WholeFileDecoders"/>
<Func Name="IsWholeFileEncoder" Arg="encoder"/>
<Func Name="IsWholeFileDecoder" Arg="decoder"/>
<Description>
<C>WholeFileEncoders</C> and <C>WholeFileDecoders</C> are hashsets containing functions that
encode and decode an entire file. These are functions designed for graph formats where graphs
are declared across multiple lines, such as dreadnaut.<P/>
<C>IsWholeFileEncoder</C> and <C>IsWholeFileDecoder</C> are functions that check whether a given
argument belongs to the hashsets <C>WholeFileEncoders</C> and <C>WholeFileDecoders</C>, respectively. <P/>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label="DIMACSString">
<ManSection>
<Oper Name="DIMACSString" Arg="digraph"/>
<Oper Name="DigraphFromDIMACSString" Arg="s"/>
<Returns>A string.</Returns>
<Description>
<C>DIMACSString</C> takes a single symmetric digraph <A>digraph</A>, and returns a string
representation of <A>digraph</A> in the DIMACS format. <P/>
<C>DigraphFromDIMACSString</C> takes such a string and returns the single symmetric digraph which it describes. <P/>
For more information on the DIMACS format, see <Ref Oper="WriteDIMACSDigraph"/>.<P/>
These functions support file-based DIMACS encoding and decoding through <Ref Func="WriteDigraphs"/> and <Ref Func="ReadDigraphs"/>,
for consistency with other encoders and decoders. Alternatively, <Ref Oper="WriteDIMACSDigraph"/> and <Ref Oper="ReadDIMACSDigraph"/> may be used for direct DIMACS I/O.
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