From 6f9e1680085e7bb4d258f6f8116369d122e196e1 Mon Sep 17 00:00:00 2001
From: Norbert Preining <norbert@preining.info>
Date: Mon, 16 Jan 2023 03:03:27 +0000
Subject: CTAN sync 202301160303

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+% Copyright 2019 by Renée Ahrens, Olof Frahm, Jens Kluttig, Matthias Schulz, Stephan Schuster
+% Copyright 2019 by Till Tantau
+% Copyright 2019 by Jannis Pohlmann
+%
+% 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{Introduction to Algorithmic Graph Drawing}
+\label{section-intro-gd}
+
+\emph{by Till Tantau}
+
+\ifluatex
+\else
+    This section of the manual can only be typeset using Lua\TeX.
+    \expandafter\endinput
+\fi
+
+
+\subsection{What Is Algorithmic Graph Drawing?}
+
+\emph{Algorithmic graph drawing} (or just \emph{graph drawing} in the
+following) is the process of computing algorithmically where the nodes of a
+graph are positioned on a page so that the graph ``looks nice''. The idea is
+that you, as human (or you, as a machine, if you happen to be a machine and
+happen to be reading this document) just specify which nodes are present in a
+graph and which edges are present. Additionally, you may add some ``hints''
+like ``this node should be near the center'' or ``this edge is pretty
+important''. You do \emph{not} specify where, exactly, the nodes and edges
+should be. This is something you leave to a \emph{graph drawing algorithm}. The
+algorithm gets your description of the graph as an input and then decides where
+the nodes should go on the page.
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing}
+\usegdlibrary{trees}}]
+\tikz \graph [binary tree layout, level distance=5mm] {
+  4 -- {
+    3 -- 0 -- 1[second],
+    10 -- {
+      8 -- {
+        6 -- {5,7},
+        9
+  } } }
+};
+\end{codeexample}
+
+\begin{codeexample}[preamble={\usetikzlibrary{graphs,graphdrawing,quotes}
+\usegdlibrary{force}}]
+\tikz \graph [spring layout,
+  edge quotes mid,
+  edges={nodes={font=\scriptsize, fill=white, sloped, inner sep=1pt}}]
+{
+  1 ->["Das"] 2 ->["ist"] 3 ->["das"] 4 ->["Haus"]
+  2 ->["vom" near start] 5 ->["Ni"] 4 ->["ko" near start]
+  1 ->["laus", orient=right] 5;
+};
+\end{codeexample}
+
+Naturally, graph drawing is a bit of a (black?) art. There is no ``perfect''
+way of drawing a graph, rather, depending on the circumstances there are
+several different ways of drawing the same graph and often it will just depend
+on the aesthetic sense of the reader which layout he or she would prefer. For
+this reason, there are a huge number of graph drawing algorithms ``out there''
+and there are scientific conference devoted to such algorithms, where each year
+dozens of new algorithms are proposed.
+
+Unlike the rest of \pgfname\ and \tikzname, which is implemented purely in
+\TeX, the graph drawing algorithms are simply too complex to be implemented
+directly in \TeX. Instead, the programming language Lua is used by the
+|graphdrawing| library -- a programming language that has been integrated into
+recent versions of \TeX. This means that (a) as a user of the graph drawing
+engine you run \TeX\ on your documents in the usual way, no external programs
+are called since Lua is already integrated into \TeX, and (b) it is pretty easy
+to implement new graph drawing algorithms for \tikzname\ since Lua can be used
+and no \TeX\ programming knowledge is needed.
+
+
+\subsection{Using the Graph Drawing System}
+
+``Users'' of the graph drawing engine can invoke the graph drawing algorithms
+often by just adding a single option to their picture. Here is a typical
+example, where the |layered layout| option tells \tikzname\ that the graph
+should be drawn (``should be laid out'') using a so-called ``layered graph
+drawing algorithm'' (what these are will be explained later):
+%
+\begin{codeexample}[preamble={\usetikzlibrary{arrows.meta,graphs,graphdrawing}
+\usegdlibrary{layered}}]
+\tikz [>={Stealth[round,sep]}]
+  \graph [layered layout, components go right top aligned, nodes=draw, edges=rounded corners]
+  {
+    first root -> {1 -> {2, 3, 7} -> {4, 5}, 6 }, 4 -- 5;
+    second root -> x -> {a -> {u,v}, b, c -> d -> {w,z} };
+    third root -> child -> grandchild -> youngster -> third root;
+  };
+\end{codeexample}
+%
+Here is another example, where a different layout method is used that is more
+appropriate for trees:
+%
+\begin{codeexample}[preamble={\usetikzlibrary{graphdrawing}
+\usegdlibrary{trees}}]
+\tikz [grow'=up, binary tree layout, nodes={circle,draw}]
+  \node {1}
+  child { node {2}
+    child { node {3} }
+    child { node {4}
+      child { node {5} }
+      child { node {6} }
+    }
+  }
+  child { node {7}
+    child { node {8}
+      child[missing]
+      child { node {9} }
+    }
+  };
+\end{codeexample}
+%
+A final example, this time using a ``spring electrical layout'' (whatever that
+might be\dots):
+%
+\begin{codeexample}[
+    preamble={\usetikzlibrary{decorations.pathmorphing,graphdrawing}
+\usegdlibrary{force}}]
+\tikz [spring electrical layout, node distance=1.3cm,
+       every edge/.style={
+         decoration={coil, aspect=-.5, post length=1mm,
+                     segment length=1mm, pre length=2mm},
+         decorate, draw}]
+{
+  \foreach \i in {1,...,6}
+    \node (node \i) [fill=blue!50, text=white, circle] {\i};
+
+  \draw (node 1) edge (node 2)
+        (node 2) edge (node 3)
+                 edge (node 4)
+        (node 3) edge (node 4)
+                 edge (node 5)
+                 edge (node 6);
+}
+\end{codeexample}
+%
+In all of the example, the positions of the nodes have only been computed
+\emph{after} all nodes have been created and the edges have been specified. For
+instance, in the last example, without the option |spring electrical layout|,
+all of the nodes would have been placed on top of each other.
+
+
+\subsection{Extending the Graph Drawing System}
+
+The graph drawing engine is also intended to make is (relatively) easy to
+implement new graph drawing algorithms. These algorithms can either be
+implemented in the Lua programming language (which is \emph{much} easier to
+program than \TeX\ itself) or in C/C++ (but at a great cost regarding
+portability). The Lua code for a graph drawing algorithm gets an
+object-oriented model of the input graph as an input and must just compute the
+desired new positions of the nodes. The complete handling of passing options
+and configurations back-and-forth between the different \tikzname\ and
+\pgfname\ layers is handled by the graph drawing engine.
+
+As a caveat, the graph drawing engine comes with a library of functions and
+methods that simplify the writing of new graph drawing algorithms. As a typical
+example, when you implement a graph drawing algorithm for trees, you typically
+require that your input is a tree; but you can bet that users will feed all
+sorts of graphs to your algorithm, including disjoint unions of cliques. The
+graph drawing engine offers you to say that a precondition to running your
+algorithm is that the graph is a |tree| and instead of the original graph your
+algorithm will be provided with a spanning tree of the graph on which it can
+work. There are numerous further automatic pre- and postprocessing steps that
+include orienting, anchoring, and packing of components, to name a few.
+
+The bottom line is that the graph drawing engine makes it easy
+to try out new graph drawing algorithms for medium sized graphs (up
+to a few hundred nodes) in Lua. For larger graphs, C/C++ code must be
+used.
+
+
+\subsection{The Layers of the Graph Drawing System}
+\label{section-gd-layers}
+
+Even though the graph drawing system presented in the following sections was
+developed as part of \pgfname, it can be used independently of \pgfname\ and
+\tikzname: It was (re)designed so that it can be used by arbitrary programs as
+long as they are able to run Lua. To achieve this, the graph drawing system
+consists of three layers:
+%
+\begin{enumerate}
+    \item At the ``bottom'' we have the \emph{algorithmic layer}. This layer,
+        written in Lua, contains all graph drawing algorithms. Interestingly,
+        options must also be declared on this layer, so an algorithm together
+        with all options it uses can and must be specified entirely on this
+        layer. If you intend to implement a new graph drawing algorithm, you
+        will only be interested in the functionality of this layer.
+
+        Algorithm ``communicate'' with the graph drawing system through a
+        well-defined interface, encapsulated in the class
+        |InterfaceToAlgorithms|.
+    \item At the ``top'' we have the \emph{display layer}. This layer is not
+        actually part of the graph drawing system. Rather, it is a piece of
+        software that ``displays'' graphs and \tikzname\ is just one example of
+        such a software. Another example might be a graph editor that uses the
+        graph drawing system to lay out the graph it displays. Yet another
+        example might be a command line tool for drawing graphs described in a
+        file. Finally, you may also wish to use the graph drawing system as a
+        simple subroutine for rendering graphs produced in a larger program.
+
+        Since the different possible instantiations of the display layer are
+        quite heterogeneous, all display layers must communicate with the graph
+        drawing system through a special interface, encapsulated in the class
+        |InterfaceToDisplay|.
+
+        The main job of this class is to provide a set of methods for
+        specifying that a graph has certain nodes and edges and that certain
+        options have been set for them. However, this interface also allows you
+        to query all options that have been declared by algorithms, including
+        their documentation. This way, an editor or a command line tool can
+        display a list of all graph drawing algorithms and how they can be
+        configured.
+    \item The algorithm layer and the display layer are ``bound together''
+        through the \emph{binding layer}. Most of the bookkeeping concerning
+        the to-be-drawn graphs is done by the graph drawing system
+        independently of which algorithm is used and also independently of
+        which display layer is used, but some things are still specific to each
+        display layer. For instance, some algorithms may create new nodes and
+        the algorithms may then need to know how large these nodes will be. For
+        this, the display layer must be ``queried'' during a run of the
+        algorithm -- and it is the job of the binding layer to achieve this
+        callback.
+
+        As a rule, the binding layer implements the ``backward'' communication
+        from the graph drawing system back to the display layer, while the
+        display layer's interface class provides only functions that are called
+        from the display layer but which will not ``talk back''.
+\end{enumerate}
+
+All of the files concerned with graph drawing reside in the |graphdrawing|
+subdirectory of |generic/pgf|.
+
+
+\subsection{Organisation of the Graph Drawing Documentation}
+
+The documentation of the graph drawing engine is structured as follows:
+%
+\begin{enumerate}
+    \item Following this overview section, the next section documents the graph
+        drawing engine from ``the \tikzname\ user's point of view''. No
+        knowledge of Lua or algorithmic graph drawing is needed for this
+        section, everyone who intends to use algorithmic graph drawing in
+        \tikzname\ may be interested in reading it.
+    \item You will normally only use \tikzname's keys and commands in order to
+        use the graph drawing system, but, internally, these keys call more
+        basic \pgfname\ commands that do the ``hard work'' of binding the world
+        of \TeX\ boxes and macros to the object-oriented world of Lua.
+        Section~\ref{section-gd-pgf} explains how this works and which commands
+        are available for authors of packages that directly need to use the
+        graph drawing system inside \pgfname, avoiding the overhead incurred by
+        \tikzname.
+
+        Most readers can safely skip this section.
+    \item The next sections detail which graph drawing algorithms are currently
+        implemented as part of the \tikzname\ distribution, see
+        Sections~\ref{section-first-graphdrawing-library-in-manual}
+        to~\ref{section-last-graphdrawing-library-in-manual}.
+    \item Section~\ref{section-gd-algorithm-layer} is addressed at readers who
+        wish to implement their own graph drawing algorithms. For this,
+        \emph{no knowledge at all} of \TeX\ programming is needed. The section
+        explains the graph model used in Lua, the available libraries, the
+        graph drawing pipeline, and everything else that is part of the Lua
+        side of the engine.
+    \item Section~\ref{section-gd-display-layer} details the display layer of
+        the graph drawing system. You should read this section if you wish to
+        implement a new display system (that is, a non-\TeX-based program) that
+        intends to use the graph drawing system.
+    \item Section~\ref{section-gd-binding-layer} explains how binding layers
+        can be implemented. This section, too, is of interest only to readers
+        who wish to write new display systems.
+\end{enumerate}
+
+
+\subsection{Acknowledgements}
+
+Graph drawing in \tikzname\ began as a student's project under my supervision.
+Ren\'ee Ahrens, Olof-Joachim Frahm, Jens Kluttig, Matthias Schulz, and Stephan
+Schuster wrote the first prototype of a graph drawing system inside \tikzname\
+that uses Lua\TeX\ for the implementation of graph drawing algorithms.
+
+This first, early version was greatly extended on the algorithmic side by
+Jannis Pohlmann who wrote his Diploma thesis on graph drawing under my
+supervision. He implemented, in particular, the Sugiyama method
+(|layered layout|) and force based algorithms. Also, he rewrote some of the
+code of the prototype.
+
+At some point it became apparent that the first implementation had a number of
+deficiencies, both concerning the structure, the interfaces, and (in
+particular) the performance. Because of this, I rewrote the code of the graph
+drawing system, both on the \TeX\ side and on the Lua side in its current form.
+However, I would like to stress that without the work of the people mentioned
+above graph drawing in \tikzname\ would not exist.
+
+The documentation was written almost entirely by myself, though I did copy some
+paragraphs from Jannis's Diploma thesis, which I can highly recommend everyone
+to read.
+
+In the future, I hope that other people will contribute algorithms, which will
+be available as libraries.
-- 
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