\section{Graphs and matrices}
%<-------------------------------------------------------------------------->
\subsection{The adjacency matrix of a graph: \tkzcname{tkzAdjacencyMatrix}}
\begin{NewMacroBox}{tkzAdjacencyMatrix}{\oarg{local options}}
\begin{tabular}{llc}
\toprule
Options   & Default  & Definition           \\
\midrule
\TOline{directed} {false} {an edge A--B counts only for the entry (A,B)}
\TOline{order}    {\{\}}  {order of the vertices: \tkzname{order=\{A,B,C\}}}
\bottomrule
\end{tabular}

\medskip
\emph{Writes the adjacency matrix of the graph drawn in the last
\tkzname{tikzpicture}. Each picture records its vertices (in order of
creation) and its edges. The entry $(i,j)$ is the number of edges between
the $i$-th and the $j$-th vertex; a loop counts $1$. The macro can be used in
text mode or in math mode.}
\end{NewMacroBox}

\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
  \Vertices[unit=1.5]{circle}{A,B,C,D}
  \Edges(A,B,C,D,A)
  \Edge(A)(C)
  \Loop[dir=EA,dist=1.5cm](A)
\end{tikzpicture}

$M = \tkzAdjacencyMatrix$

\tkzAdjacencyMatrix[order={D,C,B,A}]
\end{tkzexample}

With \tkzname{tkz-berge}:

\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=.5]
  \GraphInit[vstyle=Art]
  \grCycle[RA=2]{5}
\end{tikzpicture}
\quad $C_5\colon \tkzAdjacencyMatrix$
\end{tkzexample}

\subsection{A graph from a matrix: \tkzcname{tkzGraphFromMatrix}}
\begin{NewMacroBox}{tkzGraphFromMatrix}{\oarg{local options}\var{list of vertices}\var{matrix}}
\begin{tabular}{llc}
\toprule
Options   & Default  & Definition           \\
\midrule
\TOline{placed}        {false}{the vertices already exist}
\TOline{unit}          {\textbackslash GraphUnit}{radius of the circle}
\TOline{rotation}      {0}    {angle of the first vertex}
\TOline{clockwise}     {false}{the vertices turn clockwise}
\TOline{directed}      {false}{arrows; i$\to$j and j$\to$i are bent}
\TOline{weighted}      {false}{the entries are written on the edges}
\TOline{style}         {\{\}} {\TIKZ\ options added to each edge}
\TOline{bend}          {15}   {angle of the bent edges}
\TOline{loop distance} {1cm}  {size of the loops}
\bottomrule
\end{tabular}

\medskip
\emph{The rows of the matrix are separated by \tkzname{;} and the entries
by \tkzname{,} (use a decimal point). A non-zero entry $(i,j)$ gives an edge
between the $i$-th and the $j$-th vertex, a non-zero entry on the diagonal a
loop, directed away from the center of the graph. Without
\tkzname{placed}, the vertices are placed on a circle, like
\tkzcname{Vertices}\tkzname{\{circle\}}; the options of the vertices
(\tkzcname{SetVertexMath}, \tkzcname{GraphInit}\dots) apply. Without
\tkzname{directed}, only the upper triangle of the matrix is read.}
\end{NewMacroBox}

\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
  \tkzGraphFromMatrix[unit=1.5,rotation=90]%
    {A,B,C,D}{0,1,1,0;
              1,0,1,1;
              1,1,0,1;
              0,1,1,1}
\end{tikzpicture}
\end{tkzexample}

\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
  \tkzGraphFromMatrix[directed,weighted,
                      unit=2]%
    {1,2,3}{0,4,0; 2,0,7; 5,0,0}
\end{tikzpicture}
\end{tkzexample}

\subsubsection{Placed vertices}
With \tkzname{placed}, the vertices are drawn first, anywhere.

\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
  \GraphInit[vstyle=Shade]
  \Vertices[unit=2]{square}{A,B,C,D}
  \tkzGraphFromMatrix[placed]%
    {A,B,C,D}{0,1,1,1;
              1,0,1,0;
              1,1,0,1;
              1,0,1,0}
\end{tikzpicture}
\end{tkzexample}

\endinput