[Tex/LaTex] TikZ automata: size of circle around nodes

Question

I am trying to replace vaucanson-g with TikZ, but I cannot make the automata as small. There seems to be a minimum size of the circle around nodes, that I can't reduce even with inner sep=0. Example below:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{automata,positioning}
\begin{document}
\begin{tikzpicture} [->,auto,node distance=0.6cm,line width=0.4mm]
 \node[state,initial,inner sep=1pt] (q) {$q$};
 \node[state,accepting] (p) [right=of q] {$p$};
\end{tikzpicture}
\end{document}

A lot of whitespace is left around the letters.

Answer 1

Adding inner sep=0pt, minimum size=0pt does the job for me.

Here is the full code:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{automata,positioning}
\begin{document}
\begin{tikzpicture} [->,auto,node distance=0.6cm,line width=0.4mm]
 \node[state,initial,inner sep=1pt,minimum size=0pt] (q) {$q$};
 \node[state,accepting,inner sep=1pt,minimum size=0pt] (p) [right=of q] {$p$};
\end{tikzpicture}
\end{document}