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+% Copyright 2019 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Free Documentation License.
+%
+% See the file doc/generic/pgf/licenses/LICENSE for more details.
+
+
+\section{Using Graph Drawing in \tikzname}
+
+{\noindent {\emph{by Till Tantau}}}
+
+\begin{tikzlibrary}{graphdrawing}
+ This package provides capabilities for automatic graph drawing. It requires
+ that the document is typeset using Lua\TeX. This package should work with
+ Lua\TeX\ 0.54 or higher.
+\end{tikzlibrary}
+
+\ifluatex
+\else
+ This section of the manual can only be typeset using Lua\TeX.
+ \expandafter\endinput
+\fi
+
+
+\subsection{Choosing a Layout and a Library}
+
+The graph drawing engine is initialized when you load the library
+|graphdrawing|. This library provides the basic framework for graph drawing,
+including all options and keys described in the present section. However, this
+library does \emph{not} load any actual algorithms for drawing graphs. For
+this, you need to use the following command, which is defined by the
+|graphdrawing| library:
+
+\begin{command}{\usegdlibrary\marg{list of libraries}}
+ This command is used to load the special graph drawing libraries (the |gd|
+ in the name of the command stands for ``graph drawing''). The \meta{list of
+ libraries} is a comma-separated list of library written in the Lua
+ programming language (which is why a special command is needed).
+
+ In detail, this command does the following. For each \meta{name} in the
+ \meta{list of libraries} we do:
+ %
+ \begin{enumerate}
+ \item Check whether Lua\TeX\ can call |require| on the library file
+ |pgf.gd.|\meta{name}|.library|. Lua\TeX's usual file search
+ mechanism will search the texmf-trees in the usual manner and the
+ dots in the file name get converted into directory slashes.
+ \item If the above failed, try to |require| the string
+ |pgf.gd.|\meta{name}.
+ \item If this fails, try to |require| the string \meta{name}|.library|.
+ \item If this fails, try to |require| the string \meta{name}. If this
+ fails, print an error message.
+ \end{enumerate}
+ %
+ The net effect of the above is the following: Authors of graph drawing
+ algorithms can bundle together multiple algorithms in a library by creating
+ a |...xyz/library.lua| file that internally just calls |require| for all
+ files containing declarations. On the other hand, if a graph drawing
+ algorithm completely fits inside a single file, it can also be read
+ directly using |\usegdlibrary|.
+ %
+\begin{codeexample}[code only]
+\usetikzlibrary{graphdrawing}
+\usegdlibrary{trees,force}
+\end{codeexample}
+
+ The different graph drawing libraries are documented in the following
+ Sections~\ref{section-first-graphdrawing-library-in-manual} to
+ \ref{section-last-graphdrawing-library-in-manual}.
+\end{command}
+
+Note that in addition to the graph \emph{drawing} libraries, you may also wish
+to load the normal \tikzname\ library |graphs|. It provides the powerful
+|graph| path command with its easy-to-use syntax for specifying graphs, but you
+can use the graph drawing engine independently of the |graphs| library, for
+instance in conjunction with the |child| or the |edge| syntax. Here is a
+typical setup:
+%
+\begin{codeexample}[code only]
+\usetikzlibrary{graphs, graphdrawing}
+\usegdlibrary{trees, layered}
+\end{codeexample}
+
+Having set things up, you must then specify for which scopes the graph drawing
+engine should apply a layout algorithm to the nodes in the scope. Typically,
+you just add an option ending with |... layout| to the |graph| path operation
+and then let the graph drawing do its magic:
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{layered}}]
+\tikz [rounded corners]
+ \graph [layered layout, sibling distance=8mm, level distance=8mm]
+ {
+ a -> {
+ b,
+ c -> { d, e }
+ } ->
+ f ->
+ a
+ };
+\end{codeexample}
+
+Whenever you use such an option, you can:
+%
+\begin{itemize}
+ \item Create nodes in the usual way. The nodes will be created completely,
+ but then tucked away in an internal table. This means that all of
+ \tikzname's options for nodes can be applied. You can also name a node
+ and reference it later.
+ \item Create edges using either the syntax of the |graph| command (using
+ |--|, |<-|, |->|, or |<->|), or using the |edge| command, or using the
+ |child| command. These edges will, however, not be created immediately.
+ Instead, the basic layer's command |\pgfgdedge| will be called, which
+ stores ``all the information concerning the edge''. The actual drawing
+ of the edge will only happen after all nodes have been positioned.
+ \item Most of the keys that can be passed to an edge will work as expected.
+ In particular, you can add labels to edges using the usual |node|
+ syntax for edges.
+ \item The |label| and |pin| options can be used in the usual manner with
+ nodes inside a graph drawing scope. Only, the labels and nodes will
+ play no role in the positioning of the nodes and they are added when
+ the nodes are finally positioned.
+ \item Similarly, nodes that are placed ``on an edge'' using the implicit
+ positioning syntax can be used in the usual manner.
+\end{itemize}
+%
+Here are some things that will \emph{not} work:
+%
+\begin{itemize}
+ \item Only edges created using the graph syntax, the |edge| command, or the
+ |child| command will correctly pass their connection information to the
+ basic layer. When you write |\draw (a)--(b);| inside a graph drawing
+ scope, where |a| and |b| are nodes that have been created inside the
+ scope, you will get an error message / things will look wrong. The
+ reason is that the usual |--| is not ``caught'' by the graph drawing
+ engine and, thus, tries to immediately connect two nodes that do not
+ yet exist (except inside some internal table).
+ \item The options of edges are executed twice: Once when the edge is
+ ``examined'' by the |\pgfgdedge| command (using some magic to shield
+ against the side effects) and then once more when the edge is actually
+ created. Fortunately, in almost all cases, this will not be a problem;
+ but if you do very evil magic inside your edge options, you must roll a
+ D100 to see what strange things will happen. (Do no evil, by the way.)
+\end{itemize}
+
+If you are really interested in the ``fine print'' of what happens, please see
+Section~\ref{section-gd-pgf}.
+
+
+\subsection{Graph Drawing Parameters}
+
+Graph drawing algorithms can typically be configured in some way. For instance,
+for a graph drawing algorithm that visualizes its nodes as a tree, it will
+typically be useful when the user can change the so-called \emph{level
+distance} and the \emph{sibling distance}. For other algorithms, like
+force-based algorithms, a large number of parameters influence the way the
+algorithms work. Options that influence graph drawing algorithms will be called
+\emph{(graph drawing) parameters} in the following. From the user's point of
+view, these parameters look like normal \tikzname\ keys and you set them in the
+usual way. Internally, they are treated a bit differently from normal keys
+since their ``effect'' becomes apparent only later on, namely during the run of
+the graph drawing algorithm.
+
+A graph drawing algorithm may or may not take different graph parameters into
+account. After all, these options may even outright contradict each other, so
+an algorithm can only try to ``do its best''. While many graph parameters are
+very specific to a single algorithm, a number of graph parameters will be
+important for many algorithms and they are documented in the course of the
+present section. Here is an example of an option the ``always works'':
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{force}}]
+\tikz \graph [spring layout, vertical=1 to 2] { 1--2--3--1 };
+\end{codeexample}
+
+\includeluadocumentationof{pgf.gd.control.Distances}
+\includeluadocumentationof{pgf.gd.control.Anchoring}
+\includeluadocumentationof{pgf.gd.control.Orientation}
+
+\includeluadocumentationof{pgf.gd.control.FineTune}
+
+\includeluadocumentationof{pgf.gd.control.Components}
+\includeluadocumentationof{pgf.gd.control.ComponentOrder}
+\includeluadocumentationof{pgf.gd.control.ComponentDirection}
+\includeluadocumentationof{pgf.gd.control.ComponentAlign}
+\includeluadocumentationof{pgf.gd.control.ComponentDistance}
+
+\includeluadocumentationof{pgf.gd.control.NodeAnchors}
+
+\includeluadocumentationof{pgf.gd.model.Hyperedge}
+
+
+\subsection{Using Several Different Layouts to Draw a Single Graph}
+\label{section-gd-sublayouts}
+
+Inside each graph drawing scope, a main algorithm is used to perform the graph
+drawing. However, parts of the graph may be drawn using different algorithms:
+For instance, a graph might consist of several, say, cliques that are arranged
+in a tree-like fashion. In this case, it might be useful to layout each clique
+using a circular layout, but then lay out all laid out cliques using a tree
+drawing algorithm.
+
+In order to lay out a graph using multiple algorithms, we need two things:
+First, we must be able to \emph{specify} which algorithms should be used where
+and, second, we must be able to \emph{resolve} conflicts that may result from
+different algorithms ``having different ideas'' concerning where nodes should
+be placed.
+
+
+\subsubsection{Sublayouts}
+
+Specifying different layouts for a graph is easy: Inside a graph drawing scope,
+simply open scopes, in which you use an option like |tree layout| for the nodes
+mentioned in this scope. Inside these scopes, you can open even subscopes for
+sublayouts, and so on. Furthermore, the |graphs| library has special support
+for sublayouts.
+
+Let us start with the ``plain'' syntax for opening sublayouts: You pass a key
+for creating layouts to a |scope|:
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphdrawing}
+\usegdlibrary{force,trees}}]
+\tikz [spring layout] {
+ \begin{scope}[tree layout]
+ \node (a) {a};
+ \node (b) {b};
+ \node (c) {c};
+ \draw (a) edge (b) edge (c);
+ \end{scope}
+
+ \begin{scope}[tree layout]
+ \node (1) {1};
+ \node (2) {2};
+ \draw (1) edge (2);
+ \end{scope}
+
+ \draw (a) edge (1);
+}
+\end{codeexample}
+
+Let us see, what is going on here. The main layout (|spring layout|) contains
+two sublayouts (the two |tree layouts|). Both of them are laid out
+independently (more on the details in a moment). Then, from the main layout's
+point of view, the sublayouts behave like ``large nodes'' and, thus, the edge
+between |a| and |1| is actually the only edge that is used by the
+|spring layout| -- resulting in a simple layout consisting of one big node at
+the top and a big node at the bottom.
+
+The |graphs| library has a special support for sublayouts: The syntax is as
+follows: wherever a normal node would go, you can write
+%
+\begin{quote}
+ |//| \opt{\oarg{layout options}} |{|\meta{sublayout}|}|
+\end{quote}
+
+Following the double slash, you may provide \meta{layout options} in square
+brackets. However, you \emph{must} provide a sublayout in braces. The contents
+of \meta{sublayout} will be parsed using the usual |graph| syntax, but will
+form a sublayout.
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{force,trees}}]
+\tikz \graph [spring layout] {
+ // [tree layout] { a -- {b, c} };
+ // [tree layout] { 1 -- 2 };
+ a -- 1;
+};
+\end{codeexample}
+
+In the above example, there is no node before the double slash, which means
+that the two sublayouts will be part of the main graph, but will not be
+indicated otherwise.
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{circular,trees}}]
+\tikz \graph [simple necklace layout] {
+ // [simple necklace layout] { a -> b -> c -> d -> e -> f -> a };
+
+ // [tree layout] { % first tentacle
+ a -> {1, 2};
+ };
+
+ // [tree layout] {% second tentacle
+ d -> {3, 4 -> {5, 6}}
+ };
+};
+\end{codeexample}
+
+In the above example, the first sublayout is the one for the nodes with letter
+names. These nodes are arranged using a simple necklace layout as the sublayout
+inherits this option from the main layout. The two small trees (|a -> {1, 2}|
+and the tree starting at the |d| node) are also sublayouts, triggered by the
+|tree layout| option. They are also arranged. Then, all of the layouts are
+merged (as described later). The result is actually a single node, so the main
+layout does nothing here.
+
+Compare the above to the following code:
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{circular,trees}}]
+\tikz \graph [simple necklace layout] {
+ // [tree layout] { % first ``giant node''
+ a -> {1, 2};
+ };
+
+ a -> b -> c -> d;
+
+ // [tree layout] {% second ``giant node''
+ d -> {3, 4 -> {5, 6}}
+ },
+
+ d -> e -> f -> a;
+};
+\end{codeexample}
+
+Here, only the two trees are laid out first. They are then contracted into
+``giant nodes'' and these are then part of the set of nodes that are arranged
+by the |simple necklace layout|. For details of how this contracting works, see
+below.
+
+
+\subsubsection{Subgraph Nodes}
+
+A \emph{subgraph node} is a special kind of node that ``surrounds'' the
+vertices of a subgraph. The special property of a subgraph node opposed to a
+normal node is that it is created only after the subgraph has been laid out.
+However, the difference to a collection like |hyper| is that the node is
+available immediately as a normal node in the sense that you can connect edges
+to it.
+
+The syntax used to declare a subgraph node in a |graph| specification is as
+follows:
+%
+\begin{quote}
+ \opt{|"|}\meta{node name}\opt{|"|}\opt{|/|\opt{|"|}\meta{text}\opt{|"|}}
+ \opt{\oarg{node options}} |//| \opt{\oarg{layout options}} |{|\meta{subgraph}|}|
+\end{quote}
+
+The idea ist that a subgraph node is declared like a normal node specification,
+but is followed by a double slash and a subgraph:
+%
+\begin{codeexample}[
+ width=5cm,
+ preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{circular,trees}},
+]
+\tikz \graph [simple necklace layout] {
+ tree 1[draw, circle] // [tree layout] { a -> {1, 2}; }
+ -> b
+ -> c
+ -> tree 2[draw] // [tree layout] { d -> {3, 4 -> {5, 6} } }
+ -> e
+ -> f
+ -> tree 1;
+};
+\end{codeexample}
+
+Note how the two subgraph nodes |tree 1| and |tree 2| surround the two smaller
+trees. In the example, both had trees as contents and these trees were rendered
+using a sublayout. However, a subgraph layout does not need to have its own
+layout: If you do \emph{not} provide a layout name after the double slash, the
+subgraph node will simply surround all nodes that were placed by the main
+layout wherever they were placed:
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{trees}}]
+\tikz [subgraph text bottom=text centered,
+ subgraph nodes={font=\itshape}]
+ \graph [tree layout] {
+ a -> { b -> {c, d}, e -> {f, g -> h} };
+
+ left [draw] // { b, c, d };
+ right [draw] // { e, f, g, h};
+
+ left <-> right;
+ };
+\end{codeexample}
+
+Every time a subgraph node is created, the following style is execute:
+
+\begin{key}{/tikz/every subgraph node}
+ Set a subgraph node style.
+\end{key}
+
+\begin{key}{/tikz/subgraph nodes=\meta{style}}
+ Sets the |every subgraph node| style to \meta{style}.
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{trees}}]
+\tikz [subgraph text bottom=text centered,
+ subgraph nodes=red]
+ \graph [tree layout] {
+ a -> { b -> {c, d}, e -> {f, g -> h} };
+
+ left [draw] // { b, c, d };
+ right [draw] // { e, f, g, h};
+
+ left <-> right;
+ };
+\end{codeexample}
+ %
+\end{key}
+
+\begin{key}{/tikz/subgraph text none}
+ When this option is used, the text of a subgraph node is not shown. Adding
+ a slash after the node name achieves roughly the same effect, but this
+ option is useful in situations when subgraph nodes generally should not
+ have any text inside them.
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{trees}}]
+\tikz [subgraph text none]
+ \graph [tree layout] {
+ a -> { b -> {c, d}, e -> {f, g -> h} };
+
+ left [draw] // { b, c, d };
+ right [draw] // { e, f, g, h};
+
+ left <-> right;
+ };
+\end{codeexample}
+ %
+\end{key}
+
+\begin{key}{/tikz/subgraph text top=\meta{text alignment options} (default text ragged right)}
+ Specifies that the text of a subgraph node should be placed at the top of
+ the subgraph node: Still inside the node, but above all nodes inside the
+ subgraph node.
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{trees}}]
+\tikz [subgraph text top=text ragged left]
+ \graph [tree layout] {
+ a -> { b -> {c, d}, e -> {f, g -> h} };
+
+ left [draw] // { b, c, d };
+ right [draw] // { e, f, g, h};
+
+ left <-> right;
+ };
+\end{codeexample}
+ %
+ You can pass any of the \meta{text alignment options} understood by
+ \tikzname, such as |text centered|:
+ %
+\begin{codeexample}[
+ width=5cm,
+ preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{trees}},
+]
+\tikz [subgraph text top=text centered]
+ \graph [tree layout] {
+ a -> { b -> {c, d}, e -> {f, g -> h} };
+
+ left [draw, circle] // { b, c, d };
+ };
+\end{codeexample}
+ %
+ To place a label \emph{outside} the subgraph node, use a label, typically
+ defined using the |quotes| library:
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing,quotes}
+\usegdlibrary{trees}}]
+\tikz \graph [tree layout] {
+ a -> { b -> {c, d}, e -> {f, g -> h} };
+
+ / ["left", draw] // { b, c, d } <->
+ / ["right", draw] // { e, f, g, h};
+ };
+\end{codeexample}
+ %
+\end{key}
+
+\begin{key}{/tikz/subgraph text bottom=\meta{text alignment options} (default ragged right)}
+ Works like |subgraph text top|, only the text placed at the bottom.
+\end{key}
+
+Note that there are no keys |subgraph text left| or |... right|, for somewhat
+technical reasons.
+
+\begin{key}{/tikz/subgraph text sep=\meta{dimension} (initially .1em)}
+ Some space added between the inner nodes of a subgraph node and the text
+ labels.
+\end{key}
+
+
+\subsubsection{Overlapping Sublayouts}
+\label{section-gd-layout-resolve}
+
+Nodes and edges can be part of several layouts. This will inevitably lead to
+conflicts because algorithm will disagree on where a node should be placed on
+the canvas. For this reason, there are some rules governing how such conflicts
+are resolved: Given a layout, starting with the main layout, the graph drawing
+system does the following:
+%
+\begin{enumerate}
+ \item We start by first processing the (direct) sublayouts of the current
+ layout (recursively). Sublayouts may overlap (they may share one or
+ more nodes), but we run the specified layout algorithm for each
+ sublayout independently on a ``fresh copy'' of all the nodes making up
+ the sublayout. In particular, different, conflicting positions may be
+ computed for nodes when they are present in several sublayouts.
+ \item Once all nodes in the sublayouts have been laid out in this way, we
+ \emph{join} overlapping elements. The idea is that if two layouts share
+ exactly one vertex, we can shift them around so that his vertex is at
+ the same position in both layouts. In more detail, the following
+ happens:
+
+ We build a (conceptual) graph whose nodes are the sublayouts and in
+ which there is an edge between two nodes if the sublayouts represented
+ by these elements have a node in common. Inside the resulting graph, we
+ treat each connected component separately. Each component has the
+ property that the sublayouts represented by the nodes in the component
+ overlap by at least one node. We now \emph{join} them as follows: We
+ start with the first sublayout in the component (``first'' with respect
+ to the order in which they appear in the input graph) and ``mark'' this
+ sublayout. We loop the following instructions as long as possible:
+ Search for the first sublayout (again, with respect to the order in
+ which they appear in the input) that is connect by an edge to a marked
+ sublayout. The sublayout will now have at least one node in common with
+ the marked sublayouts (possibly, even more). We consider the first such
+ node (again, first respect to the input ordering) and shift the whole
+ sublayout is such a way that this particular node is at the position is
+ has in the marked sublayouts. Note that after the shift, other nodes
+ that are also present in the marked sublayouts may lie at a different
+ position in the current sublayout. In this case, the position in the
+ marked sublayouts ``wins''. We then mark the sublayout.
+ \item When the above algorithm has run, we will have computed positions for
+ all nodes in all sublayouts of each of the components. For each
+ component, we contract all nodes of the component to a single node.
+ This new node will be ``large'' in the sense that its convex hull is
+ the convex hull of all the nodes in the component. All nodes that used
+ to be part of the component are removed and the new large node is added
+ (with arcs adjusted appropriately).
+ \item We now run the layout's algorithm on the resulting nodes (the
+ remaining original nodes and the contracted nodes).
+ \item In a last step, once the graph has been laid out, we expand the nodes
+ that were previously contracted. For this, the nodes that were deleted
+ earlier get reinserted, but shifted by whatever amount the contraction
+ node got shifted.
+\end{enumerate}
+
+
+\subsection{Miscellaneous Options}
+
+\includeluadocumentationof{pgf.gd.control.library}