1 files changed, 97 insertions, 0 deletions
diff --git a/vorlesungen/slides/8/pfade/adjazenz.tex b/vorlesungen/slides/8/pfade/adjazenz.tex
new file mode 100644
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+++ b/vorlesungen/slides/8/pfade/adjazenz.tex
@@ -0,0 +1,97 @@
+%
+% adjazenz.tex
+%
+% (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil
+%
+\bgroup
+\definecolor{darkred}{rgb}{0.5,0,0}
+\begin{frame}[fragile]
+\newboolean{pfeilspitzen}
+\setboolean{pfeilspitzen}{true}
+\frametitle{Adjazenz-Matrix}
+
+\begin{columns}[t]
+\begin{column}{0.48\hsize}
+\begin{center}
+\begin{tikzpicture}[>=latex]
+
+\def\r{2.2}
+\coordinate (A) at ({\r*cos(-54+0*72)},{\r*sin(-54+0*72)});
+\coordinate (C) at ({\r*cos(-54+1*72)},{\r*sin(-54+1*72)});
+\coordinate (D) at ({\r*cos(-54+2*72)},{\r*sin(-54+2*72)});
+\coordinate (B) at ({\r*cos(-54+3*72)},{\r*sin(-54+3*72)});
+\coordinate (E) at ({\r*cos(-54+4*72)},{\r*sin(-54+4*72)});
+
+\def\knoten#1#2{
+        \fill[color=white] #1 circle[radius=0.3];
+        \draw[line width=1pt] #1 circle[radius=0.3];
+        \node at #1 {$#2$};
+}
+
+\def\kante#1#2#3{
+        \ifthenelse{\boolean{pfeilspitzen}}{
+                \draw[->,line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm]
+                        #1 -- #2;
+        }{
+                \draw[line width=1pt,shorten >= 0.3cm,shorten <= 0.3cm]
+                        #1 -- #2;
+        }
+%        \fill[color=white,opacity=0.7] ($0.5*#1+0.5*#2$) circle[radius=0.22];
+%        \node at ($0.5*#1+0.5*#2$) {$#3$};
+}
+
+\kante{(A)}{(E)}{1}
+\kante{(B)}{(C)}{2}
+\kante{(B)}{(D)}{13}
+\kante{(C)}{(A)}{3}
+\kante{(D)}{(C)}{6}
+\kante{(E)}{(B)}{5}
+\kante{(E)}{(D)}{6}
+
+\knoten{(A)}{1}
+\knoten{(B)}{2}
+\knoten{(C)}{3}
+\knoten{(D)}{4}
+\knoten{(E)}{5}
+
+\end{tikzpicture}
+\end{center}
+\end{column}
+\begin{column}{0.48\hsize}
+\[
+a_{{\color{darkred}i}{\color{blue}j}}
+=
+\begin{cases}
+1&\quad\text{\# Kanten von ${\color{blue}j}$ nach ${\color{darkred}i}$}\\
+0&\quad\text{sonst}
+\end{cases}
+\]
+\begin{center}
+\begin{tikzpicture}[>=latex]
+\node at (0,0) {$\displaystyle
+A=
+\begin{pmatrix}
+0&0&1&0&0\\
+0&0&0&0&1\\
+0&1&0&1&0\\
+0&1&0&0&1\\
+1&0&0&0&0
+\end{pmatrix}
+$};
+\def\s{0.54}
+\foreach \x in {1,...,5}{
+	\node[color=blue] at ({-0.71+(\x-1)*\s},1.4) {\tiny $\x$};
+}
+\node[color=blue] at ({-0.71+2*\s},1.7) {von};
+\def\r{0.48}
+\foreach \y in {1,...,5}{
+	\node[color=darkred] at ({-0.71+5*\s},{0.02+(3-\y)*\r}) {\tiny $\y$};
+}
+\node[color=darkred] at ({-0.4+5*\s},{0.02}) [rotate=90] {nach};
+\end{tikzpicture}
+\end{center}
+\end{column}
+\end{columns}
+
+\end{frame}
+\egroup