如何绘制平面源汇网络

Question 1

我们的想法是使用其中一个包PGF/TikZ或者PS技巧. 这两个包的文档都包含大量示例。

在TeXample.net你可以找到一些可以用作 PGF/TikZ 灵感来源的代码；特别有用的是图表

在 PS-Tricks 页面中你还可以查看例子和流程图部分包含一个可能有用的示例。

编辑：这是一个TikZ可以为您提供一个起点的基本示例（使用）：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}[%
  every node/.style={draw,fill=gray!40,circle,minimum size=3pt},node distance=1cm]
  % the vertices
  \node[label=left:Source] (source) at (0,0) {1};
  \node[right=of source] (three) {3};
  \node[above=of three] (two) {2};
  \node[below=of three] (four) {4};
  \node[right=of source] (three) {3};
  \node[right=of three] (six) {6};
  \node[above=of six] (five) {5};
  \node[below=of six] (seven) {7};
  \node[right=of six,label=right:Sink] (sink) {8};
  % the edges
  \draw (source) -- (two) -- (five) -- (sink) -- (seven) -- (four) -- (source) -- (three) -- (six) -- (sink);
  \draw (two) -- (three) -- (four);
  \draw (five) -- (six) -- (seven);
\end{tikzpicture}
\end{document}

EDIT2：另一个示例包括虚线曲线和一些边缘标签，如评论中所要求的：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}
  \begin{scope}[auto,%
  every node/.style={draw,fill=gray!40,circle,minimum size=3pt},node distance=1cm]
  % the vertices
  \node[label=left:Source] (source) at (0,0) {1};
  \node[right=of source] (three) {3};
  \node[above=of three] (two) {2};
  \node[below=of three] (four) {4};
  \node[right=of source] (three) {3};
  \node[right=of three] (six) {6};
  \node[above=of six] (five) {5};
  \node[below=of six] (seven) {7};
  \node[right=of six,label=right:Sink] (sink) {8};
  \end{scope}
  % the edges
  \draw (source) -- node[label=above:4] {} (two) -- node[label=above:7] {} (five) -- node[label=above:8] {} (sink) -- (seven) -- (four) -- (source) -- (three) -- (six) -- (sink);
  \draw (two) -- (three) -- (four);
  \draw (five) -- (six) -- (seven);
  \draw[dashed] (two) to [bend right=95] (source);
  \draw[dashed] (five) to [bend left=95] (sink);
  \draw[dashed] (source) ..  controls (1,-3.5) and (4,-3.5) .. (sink);

\end{tikzpicture}

\end{document}

EDIT3：另一个例子：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}[%
  every node/.style={draw,fill=gray!40,circle,minimum size=18pt,font=\footnotesize},
  node distance=3cm,on grid]
  % the vertices
  \node[label=left:Source] (source) at (0,0) {1};
  \node[right=of source] (three) {3};
  \node[above=of three] (two) {2};
  \node[below=of three] (four) {4};
  \node[right=of source] (three) {3};
  \node[right=of three] (six) {6};
  \node[above=of six] (five) {5};
  \node[below=of six] (seven) {7};
  \node[right=of six,label=right:Sink] (sink) {8};
  \node at (1.9,1) (sfive) {$5^*$};
  \node at (4.5,1) (sseven) {$7^*$};
  \node at (7.1,1) (ssix) {$6^*$};
  \node at (1.9,-1) (sthree) {$3^*$};
  \node at (4.5,-1) (stwo) {$2^*$};
  \node at (7.1,-1) (sfour) {$4^*$};
  \node at (4.5,4) (seight) {$8^*$};
  \node at (4.5,-4) (sone) {$1^*$};
  % the edges
  \draw (source) -- (two) -- (five) -- (sink) -- (seven) -- (four) -- (source) -- (three) -- (six) -- (sink);
  \draw (two) -- (three) -- (four);
  \draw (five) -- (six) -- (seven);
  \begin{scope}[dashed]
  \draw (sfive) -- (sseven) -- (ssix) -- (sfour) -- (stwo) -- (sthree) -- (sfive);
  \draw (sthree) to [bend right=55] (sone);
  \draw (sfour) to [bend left=55] (sone);
  \draw (sfive) to [bend left=55] (seight);
  \draw (ssix) to [bend right=55] (seight);
  \draw (source) ..  controls (1,-6.5) and (8,-6.5) .. node[draw=none, fill=none,label=above:$s^*$] {} (sink);
  \end{scope}
\end{tikzpicture}

\end{document}

结果如下：

Answer