%
% inzidenz.tex
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\bgroup
\definecolor{darkgreen}{rgb}{0,0.6,0}
\begin{frame}[t]
\frametitle{Inzidenz- und Adjazenzmatrix}
\vspace{-20pt}
\begin{columns}[t,onlytextwidth]
\begin{column}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[>=latex,thick]

\def\r{2.2}

\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)});
\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)});
\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)});
\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)});
\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)});

\draw[shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (C);
\draw[color=white,line width=5pt] (B) -- (D);
{\color<2->{darkgreen}
\draw[shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (D);
}

\draw[shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (B);
\draw[shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (C);
\draw[shorten >= 0.2cm,shorten <= 0.2cm] (C) -- (D);
%\draw[shorten >= 0.2cm,shorten <= 0.2cm] (D) -- (E);
\draw[shorten >= 0.2cm,shorten <= 0.2cm] (E) -- (A);

\only<-2>{
\fill[color=white] (B) circle[radius=0.2];
}
\only<3->{
\fill[color=red!20] (B) circle[radius=0.2];
}

\draw (A) circle[radius=0.2];
\draw (B) circle[radius=0.2];
\draw (C) circle[radius=0.2];
\draw (D) circle[radius=0.2];
\draw (E) circle[radius=0.2];

\node at (A) {$1$};
\node at (B) {$2$};
\node at (C) {$3$};
\node at (D) {$4$};
\node at (E) {$5$};
\node at (0,0) {$G$};

\node at ($0.5*(A)+0.5*(B)-(0.1,0.1)$) [above right] {$\scriptstyle 1$};
\node at ($0.5*(B)+0.5*(C)+(0.05,-0.07)$) [above left] {$\scriptstyle 2$};
\node at ($0.5*(C)+0.5*(D)+(0.05,0)$) [left] {$\scriptstyle 3$};
\node at ($0.5*(E)+0.5*(A)+(-0.1,0.1)$) [below right] {$\scriptstyle 4$};
\node at ($0.6*(A)+0.4*(C)$) [above] {$\scriptstyle 5$};
{\color<2->{darkgreen}
\node at ($0.4*(B)+0.6*(D)$) [left] {$\scriptstyle 6$};
}

\end{tikzpicture}
\end{center}
\vspace{-10pt}
\uncover<5->{%
\begin{block}{Definition}
\vspace{-15pt}
\begin{align*}
B(G)_{ij}&=1&&\Leftrightarrow&&\text{Kante $j$ endet in Knoten $i$}\\
A(G)_{ij}&=1&&\Leftrightarrow&&\text{Kante zwischen Knoten $i$ und $j$}
\end{align*}
\end{block}}
\end{column}
\begin{column}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[>=latex,thick]

\def\dy{0.48}
\def\dx{0.54}


\begin{scope}
\uncover<3->{
\fill[color=red!20] (1.8,1.8) rectangle (4.75,2.15);
}
\uncover<2->{
\fill[color=darkgreen!40,opacity=0.5] (4.46,0.36) rectangle (4.79,2.65);
}
\foreach \y in {1,...,5}{
	\node[color=gray] at (5.3,{2.45-(\y-1)*\dy}) {\tiny $\y$};
}
\foreach \y in {1,...,6}{
	\node[color=gray] at ({1.92+(\y-1)*\dx},2.90) {\tiny $\y$};
}
\draw[color=gray] (1.8,2.75) -- (4.7,2.75);
\draw[color=gray] (5.2,2.55) -- (5.2,0.45);
\node[color=gray] at ({1.92+2.5*\dx},3.1) {\tiny Kanten};
\node[color=gray] at (5.3,{2.45-2*\dy}) [above,rotate=-90] {\tiny Knoten};
\end{scope}

\uncover<4->{
\begin{scope}
\uncover<3->{
\fill[color=red!20] (1.8,-1.16) rectangle (4.25,-0.77);
\fill[color=red!20] (2.3,-2.6) rectangle (2.63,-0.29);
}
\foreach \y in {1,...,5}{
	\node[color=gray] at (4.7,{-0.5-(\y-1)*\dy}) {\tiny $\y$};
	\node[color=gray] at ({1.92+(\y-1)*\dx},-0.1) {\tiny $\y$};
}
\draw[color=gray] (1.8,-0.22) -- (4.2,-0.22);
\draw[color=gray] (4.6,-0.4) -- (4.6,-2.55);
\node[color=gray] at ({1.92+2*\dx},0.1) {\tiny Knoten};
\node[color=gray] at (4.7,{-0.5-2*\dy}) [above,rotate=-90] {\tiny Knoten};
\end{scope}
}

\node (0,0) [right] {$\displaystyle
\begin{aligned}
B(G)
&=
\begin{pmatrix}
1&0&0&1&1&0\\
1&1&0&0&0&1\\
0&1&1&0&1&0\\
0&0&1&0&0&1\\
0&0&0&1&0&0
\end{pmatrix}
\\[12pt]
\uncover<4->{
A(G)
&=
\begin{pmatrix}
0&1&1&0&1\\
1&0&1&1&0\\
1&1&0&1&0\\
0&1&1&0&0\\
1&0&0&0&0
\end{pmatrix}
\end{aligned}}$};

\end{tikzpicture}
\end{center}
\end{column}
\end{columns}
\end{frame}
\egroup
