\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}

\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{tikz}
\usetikzlibrary{arrows,shapes}

\usepackage{pgfplots}

% argument #1: any options
\newenvironment{customlegend}[1][]{%
    \begingroup
    % inits/clears the lists (which might be populated from previous
    % axes):
    \csname pgfplots@init@cleared@structures\endcsname
    \pgfplotsset{#1}%
}{%
    % draws the legend:
    \csname pgfplots@createlegend\endcsname
    \endgroup
}%

% makes \addlegendimage available (typically only available within an
% axis environment):
\def\addlegendimage{\csname pgfplots@addlegendimage\endcsname}

\begin{document}
\begin{preview}
\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=3.5cm,
pflicht/.style ={rectangle, draw=blue, thick, fill=blue!20,align=center, rounded corners, minimum height=2em},
stammmodul/.style ={rectangle, draw=yellow, thick, fill=yellow!20,align=center, rounded corners, minimum height=2em},
wahl/.style ={rectangle, draw=green, thick, fill=green!20,align=center, rounded corners, minimum height=2em},
soft/.style ={rectangle, draw=red, thick, fill=red!20,align=center, rounded corners, minimum height=2em}]
    % Draw the vertices.
    \node[pflicht] (programmieren) {Programmieren};
    \node[pflicht] (gbi)    [right of=programmieren] {GBI};
    \node[pflicht] (lai)    [right of=gbi] {LA I};
    \node[pflicht] (anai)   [right of=lai]  {ANA I};

    \node[pflicht] (laii)   [below of=lai]  {LA II};
    \node[pflicht] (anaii)  [below of=anai] {ANA II};
    \node[pflicht] (algi)   [below of=gbi]   {Algorithmen I};
    \node[pflicht] (swti)   [below of=programmieren] {SWT I};
    \node[pflicht] (ro)     [right of=anaii]   {RO};

    \node[pflicht] (dt)     [below of=ro] {DT};
    \node[pflicht] (wt)     [left of=dt]  {WT};
    \node[pflicht] (tgi)    [left of=wt]  {TGI};
    \node[pflicht] (os)     [left of=tgi]  {OS};
    \node[pflicht] (pse)    [left of=os] {PSE};
    \node[soft]    (tse)    [left of=pse] {TSE};

    \node[pflicht] (numerik)    [below of=pse] {Numerik};
    \node[pflicht] (datenbanken)    [right of=numerik] {Datenbanken};
    \node[pflicht] (rechnernetze)    [below of=wt] {Rechnernetze};
    \node[stammmodul]   (KogSys)    [right of=rechnernetze] {KogSys};
    \node[stammmodul]   (Echtzeitsysteme)    [right of=KogSys] {Echtzeit-Sys.};
    \node[stammmodul]   (Rechnerstrukturen)  [right of=Echtzeitsysteme] {Rechnerstrukturen};

    \node[pflicht] (algii)  [right of=datenbanken, below of=datenbanken] {Algorithmen II};
    \node[pflicht] (propa)  [right of=algii] {Programmierparadigmen};

    \node[wahl]    (icpc)   [below of=algii] {ICPC};

    \node[wahl]    (web)    [left of=swti] {Web Engineering};


    % Connect vertices with edges and draw weights
    \path[->] (gbi)     edge[thick] node[anchor=center,above,sloped] {\tiny{Automaten}} (tgi);
    \path[->] (algi)    edge node {} (algii);
    \path[->] (tgi)     edge node[anchor=center,above,sloped] {\tiny{ILP}} (algii);
    \path[->] (tgi)     edge[red] node                        {}           (propa);
    \path[->] (wt)      edge node[anchor=center,above,sloped] {\tiny{Randomisierte Algorithmen}} (algii);
    \path[->] (wt)      edge node[anchor=center,above,sloped] {\tiny{Bayes Regel}} (KogSys);
    \path[->] (dt)      edge node[anchor=center,above,sloped] {\tiny{Zahlendarstellungen}} (ro);
    \path[->] (lai)     edge[ultra thick] node[anchor=center,above,sloped] {\tiny{Gruppe, Körper, \dots}} (laii);
    \path[<->] (lai)    edge node {} (gbi);
    \path[->] (lai)     edge node[anchor=center,above,sloped] {\tiny{Matrixmultiplikation; Lösen von linearen Gleichungssystemen}} (numerik);
    \path[->] (anai)     edge[bend left=10] node[anchor=center,above,sloped] {\tiny{Banachscher Fixpunktsatz}} (numerik);
    \path[<->] (gbi)    edge[bend left] node [anchor=center,above,sloped] {\tiny{Induktion}} (anai);
    \path[->] (anai)    edge[ultra thick] node {} (anaii);
    \path[->] (laii)    edge[bend left] node[anchor=center,above,sloped] {\tiny{Mathematische Strukturen}} (algii);
    \path[->] (programmieren)    edge[very thick] node[anchor=center,above,sloped] {\tiny{Java}} (swti);
    \path[->] (programmieren)    edge[bend left] node {} (pse);
    \path[->] (programmieren)    edge node {} (os);
    \path[->] (swti)    edge[red] node {} (pse);
    \path[<->] (ro)     edge node[anchor=center,above,sloped] {\tiny{Assembler, Adressierung, Caches}} (os);
    \path[<->] (algii)  edge [very thick] node {} (icpc);
    \path[->] (swti)    edge node[anchor=center,above,sloped] {\tiny{Prozessmodelle}} (web);
    \path[<->] (pse)    edge[red] node {} (tse);

    \path[->] (laii)    edge[red] node {} (pse);
    \path[->] (anaii)   edge[red] node {} (pse);
    \path[->] (programmieren)   edge[red, bend right] node {} (pse);
    %\path[->] (algi)    edge[red] node {} (pse);
    \path[->] (algi)    edge[bend left] node[anchor=center,above,sloped] {\tiny{B-Bäume}} (datenbanken);
    \path[->] (swti)    edge[red, bend right] node {} (pse);
    \path[->] (gbi)     edge[red] node {} (pse);
    \path[<->] (os)     edge node[anchor=center,above,sloped] {\tiny{Paging}} (algii);
    \path[->] (ro)      edge[thick] node[anchor=center,above,sloped] {\tiny{Bus, ROS, CAS, Microprozessoraufbau}} (Echtzeitsysteme);
    \path[->] (anaii)   edge[bend right] node[anchor=center,above,sloped] {\tiny{Differenzialgleichungen}} (Echtzeitsysteme);
    \path[->] (ro)   edge[bend left] node[anchor=center,above,sloped] {\tiny{Pipelining, CISC, RISC}} (Rechnerstrukturen);

    \begin{customlegend}[legend entries={Pflichtmodul,Stammmodul,Wahlmodul,Softskill,Inhaltliche Abhängigkeit,Harte Abhängigkeit},legend style={at={(-3,-12)},anchor=center}]
    \addlegendimage{blue,fill=blue!20,area legend}
    \addlegendimage{yellow,fill=yellow!20,area legend}
    \addlegendimage{green,fill=green!20,area legend}
    \addlegendimage{red,fill=red!20,area legend}
    \addlegendimage{->,black,sharp plot}
    \addlegendimage{->,red,sharp plot}
    %\addlegendimage{red,fill=black!50!red,mark=*,sharp plot}
    %\addlegendimage{red,fill=black!50!red,ybar,ybar legend}
    \end{customlegend}
\end{tikzpicture}
\end{preview}
\end{document}