How to make all vertices same size?

Question

I was wondering how to make the vertices in my graph have the same size and those horizontal arcs to be actually horizontal:

Here is my code, and feel free to make any suggestion even on other issues:

 \documentclass[12pt]{article}
 \usepackage{graphicx}
 \usepackage{subfigure}
 \usepackage{amsmath}
 \usepackage{amsfonts}

 \usepackage{tikz}
 \usetikzlibrary{positioning}

\begin{center}
\begin{tikzpicture}
  \begin{scope}[auto,%
  every node/.style={draw,fill=gray!40,circle,minimum size=3pt},node distance=2cm]
  % the vertices
  \node[label=left:Source] (source) at (0,0) {1*/0};
  \node[above left=of source] (three) {3*/20};
  \node[left=of three] (two) {2*/20};
  \node[above right=of source] (four) {4*/1};
  \node[right=of four] (five) {5*/20};
  \node[above=of two] (six) {6*/21};
  \node[above=of three] (seven) {7*/3};
  \node[above=of four] (eight) {8*/2};
  \node[above=of five] (nine) {9*/21};
  \node[above right=of seven,label=right:Sink] (sink) {11*/4};
  \end{scope}
  % the edges
  \draw (source) -- node[label=above:20] {} (two) -- node[label=right:1] {} (six) -- node[label=above:1] {} (sink) -- node[label=above:1] {} (seven) -- node[label=right:20] {} (three) -- node[label=above:20] {} (source) -- node[label=above:1] {} (four) -- node[label=right:1] {} (eight) -- node[label=above:20] {} (sink) -- node[label=above:1] {} (nine) -- node[label=right:1] {} (five) -- node[label=above:20] {} (source);
  \draw (two)  -- node[label=above:1] {} (three) -- node[label=above:20] {} (four) -- node[label=above:20] {} (five);
  \draw (six) -- node[label=above:20] {} (seven) -- node[label=above:1] {} (eight) -- node[label=above:20] {} (nine);
  \draw [red] (source) -- (four) -- (eight) --  (seven) -- (sink);
\end{tikzpicture}
\end{center}

\end{document}

Thanks and regards!

Answer 1

You have to set the minimum size=<length> key to a value which is as large as the largest circle, then all circles will have this size:

 \documentclass[12pt]{article}
 \usepackage{graphicx}
 \usepackage{subfigure}
 \usepackage{amsmath}
 \usepackage{amsfonts}

 \usepackage{tikz}
 \usetikzlibrary{positioning}

\begin{document}
\begin{tikzpicture}
  \begin{scope}[auto,%
  every node/.style={draw,fill=gray!40,circle,minimum size=4em},node distance=2cm]
  % the vertices
  \node[label=left:Source] (source) at (0,0) {1*/0};
  \node[above left=of source] (three) {3*/20};
  \node[left=of three] (two) {2*/20};
  \node[above right=of source] (four) {4*/1};
  \node[right=of four] (five) {5*/20};
  \node[above=of two] (six) {6*/21};
  \node[above=of three] (seven) {7*/3};
  \node[above=of four] (eight) {8*/2};
  \node[above=of five] (nine) {9*/21};
  \node[above right=of seven,label=right:Sink] (sink) {11*/4};
  \end{scope}
  % the edges
  \draw (source) -- node[label=above:20] {} (two) -- node[label=right:1] {} (six) -- node[label=above:1] {} (sink) -- node[label=above:1] {} (seven) -- node[label=right:20] {} (three) -- node[label=above:20] {} (source) -- node[label=above:1] {} (four) -- node[label=right:1] {} (eight) -- node[label=above:20] {} (sink) -- node[label=above:1] {} (nine) -- node[label=right:1] {} (five) -- node[label=above:20] {} (source);
  \draw (two)  -- node[label=above:1] {} (three) -- node[label=above:20] {} (four) -- node[label=above:20] {} (five);
  \draw (six) -- node[label=above:20] {} (seven) -- node[label=above:1] {} (eight) -- node[label=above:20] {} (nine);
  \draw [red] (source) -- (four) -- (eight) --  (seven) -- (sink);
\end{tikzpicture}
\end{document}