## How to visualize Graph algorithms with LaTeX

Tkiz is a very powerful TeX package. You can easily create visualizations of graphs and graph algorithms (if you have a template ). This post should give you a template to visualize graph algorithms with LaTeX.
I recently found a great animation of Prim’s algorithm done by Kjell Magne Fauske. I’ve edited his source files to show an eulerian path. This is how it looks like:

LaTeX (Tikz) animation of an eulerian path

This animation was automatically created. See Archive and the intermediate PDF.

## The ideas

### Draw the Graph

If you want to visualize a graph algorithm, you should first try to get the image of the graph with Tikz.
First include all packages / create the general structure of the document:

\documentclass[hyperref={pdfpagelabels=false}]{beamer}
\usepackage{lmodern}

\usepackage[utf8]{inputenc} % this is needed for german umlauts
\usepackage[ngerman]{babel} % this is needed for german umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf

\usepackage{verbatim}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes}

% see http://deic.uab.es/~iblanes/beamer_gallery/index_by_theme.html
\usetheme{Frankfurt}
\usefonttheme{professionalfonts}

\begin{document}
\begin{frame}
\end{frame}
\end{document}

Simple graphs could look like this:

\begin{figure}
\begin{tikzpicture}[->,scale=1.8, auto,swap]
% Draw the vertices.
\node (a) at (0,0) {$a (this is text)$};
\node (b) at (0,1) {$b$};
\node (c) at (1,1) {$c$};
\node (d) at (1,0) {$d$};
\node (e) at (3,1) {$d$};

% Connect vertices with edges and draw weights
\path (a) edge node {} (b);
\path (b) edge node {} (c);
\path (c) edge node {} (d);
\path (d) edge node {} (a);
\end{tikzpicture}
\end{figure}

You should get something similar to this:

Simple example graph created with LaTeX and Tikz

### Animate

Animations can be created with Tikz by working with layers. You don’t want to redraw the whole graph every time. Most of the time you want to overlay/underlay some parts of the graph. This can be achieved by declaring a new layer:

\pgfdeclarelayer{NAME}

Then you need to tell PGF which layers are to use in the next figure:

\pgfsetlayers{LAYER LIST}

The layer main should always be part of the list. Here is an example:

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

Now the magic begins. You consecutively add frames to the layer:

	\begin{pgfonlayer}{background}
\path<2->[draw,line width=5pt,-,red!50] (a.center) edge node {} (b.center);
\path<10->[draw,line width=5pt,-,red!50] (b.center) edge node {} (d.center);
\path<12->[draw,line width=5pt,-,red!50] (d.center) edge node {} (e.center);
\end{pgfonlayer}

The number (2, 10 and 12 in this example) indicate the frame in which it should be added. This is the absolute frame, but 1 is the first frame of the figure environment!

### Status quo

\documentclass[hyperref={pdfpagelabels=false}]{beamer}
\usepackage{lmodern}

\usepackage[utf8]{inputenc} % this is needed for german umlauts
\usepackage[ngerman]{babel} % this is needed for german umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf

\usepackage{verbatim}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes}

% see http://deic.uab.es/~iblanes/beamer_gallery/index_by_theme.html
\usetheme{Frankfurt}
\usefonttheme{professionalfonts}

\begin{document}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\begin{frame}
\begin{figure}
\begin{tikzpicture}[->,scale=1.8, auto,swap]
% Draw the vertices.
\node (a) at (0,0) {$a (this is text)$};
\node (b) at (0,1) {$b$};
\node (c) at (1,1) {$c$};
\node (d) at (1,0) {$d$};
\node (e) at (3,1) {$d$};

% Connect vertices with edges and draw weights
\path (a) edge node {} (b);
\path (b) edge node {} (c);
\path (c) edge node {} (d);
\path (d) edge node {} (a);

\begin{pgfonlayer}{background}
\path<2->[draw,line width=5pt,-,red!50] (a.center) edge node {} (b.center);
\path<10->[draw,line width=5pt,-,red!50] (b.center) edge node {} (d.center);
\path<12->[draw,line width=5pt,-,red!50] (d.center) edge node {} (e.center);
\end{pgfonlayer}
\end{tikzpicture}
\end{figure}
\end{frame}
\end{document}

### Simplify it

You can make some definitions, e.g.:

draw,line width=5pt,-,red!50

can be replaced by

\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]

You can make loops:

	% Draw the vertices.
\foreach \pos / \identifier / \name in {{(0,0)/a/a (this is text)},
{(0,1)/b/b}, {(1,1)/c/c}, {(1,0)/d/d}, {(3,1)/e/d}}
\node (\identifier) at \pos {$\name$};

## The whole, working template

\documentclass[hyperref={pdfpagelabels=false}]{beamer}
\usepackage{lmodern}

\usepackage[utf8]{inputenc} % this is needed for german umlauts
\usepackage[ngerman]{babel} % this is needed for german umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf

\usepackage{verbatim}
\usepackage{tikz}
\usetikzlibrary{arrows,shapes}

% Define some styles for graphs
\tikzstyle{vertex}=[circle,fill=black!25,minimum size=20pt,inner sep=0pt]
\tikzstyle{selected vertex} = [vertex, fill=red!24]
\tikzstyle{blue vertex} = [vertex, fill=blue!24]
\tikzstyle{edge} = [draw,thick,-]
\tikzstyle{weight} = [font=\small]
\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
\tikzstyle{ignored edge} = [draw,line width=5pt,-,black!20]

% see http://deic.uab.es/~iblanes/beamer_gallery/index_by_theme.html
\usetheme{Frankfurt}
\usefonttheme{professionalfonts}

% http://tex.stackexchange.com/questions/23727/converting-beamer-slides-to-animated-images

\begin{document}
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}

\begin{frame}
\begin{figure}
\begin{tikzpicture}[->,scale=1.8, auto,swap]
% Draw the vertices. First you define a list.
\foreach \pos/\name in {{(0,0)/a}, {(0,2)/b}, {(1,2)/c},
{(1,0)/d}, {(2,1)/e}, {(3,1)/f},
{(4,2)/g}, {(5,2)/h}, {(4,0)/i},
{(5,0)/j}}
\node[vertex] (\name) at \pos {$\name$};

% Connect vertices with edges and draw weights
\foreach \source/ \dest /\pos in {a/b/, b/c/, c/d/, d/a/,
c/e/bend left, d/e/, e/c/,
e/f/, f/g/, f/i/,
g/f/bend right, i/f/bend left,
g/h/, h/j/, j/i/, i/g/}
\path (\source) edge [\pos] node {} (\dest);

% Start animating the edge selection.
% For convenience we use a background layer to
% highlight edges. This way we don't have to worry about
% the highlighting covering weight labels.
\begin{pgfonlayer}{background}
\foreach \source / \dest / \fr / \pos in {d/a/1/,
a/b/2/, b/c/3/, c/d/4/, d/e/5/, e/c/6/,
c/e/7/bend left, e/f/8/, f/g/9/,
g/f/10/bend right, f/i/11/, i/g/12/, g/h/13/,
h/j/14/, j/i/15/, i/f/16/bend left}
\path<\fr->[selected edge] (\source.center) edge
[\pos] node {} (\dest.center);
\end{pgfonlayer}
\end{tikzpicture}
\end{figure}
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sed diam nonumy eirmod tempor invidunt ut labore et dolore
magna aliquyam erat, sed diam voluptua. At vero eos et
accusam et.
\end{frame}
\end{document}

## Resources

### 2 Responses to “How to visualize Graph algorithms with LaTeX”

1. tom says:

Du möchtest bestimmt 
ode (e) at (3,1) {$d$}; korrigieren.

Ansonsten coole Sache. Werd ich mir mal bei Zeiten genauer ansehen.

• Martin Thoma says:

Hallo Tom,

nein, dass der node e die Bezeichnung “d” bekommt, ist absicht. Ich wollte zeigen, dass hier durchaus doppelte Beschriftungen zugelassen sind.

Martin