How can I draw a circular graph in tikz?

Question

I want to draw a wheel graph which is a cycle of nodes centred on another node. What I would like is to draw edges or other paths between the cycle's nodes in a way that they form an actual circle, not some wobbly thing like this:

The code I use is this

\documentclass{standalone}
\usepackage{tikz} 
\usetikzlibrary{fit,automata,positioning,calc}

\begin{document}
   \begin{tikzpicture}
      \node[state] (center) at (0,0) {$v_0$};
      \foreach \phi in {1,...,6}{
         \node[state] (v_\phi) at (360/6 * \phi:2cm) {$v_\phi$};
         \draw (v_\phi) -- (center);
      }
      \draw[blue] (v_1) edge[bend right] (v_2);
      \draw[blue] (v_2) edge[bend right] (v_3);
      \draw[blue] (v_3) edge[bend right] (v_4);
      \draw[blue] (v_4) edge[bend right] (v_5);
      \draw[blue] (v_5) edge[bend right] (v_6);
      \draw[blue] (v_6) -- (center);
      \draw[blue] (center) -- (v_1);
   \end{tikzpicture}

\end{document}

I know I could just draw a circle centred on v0 behind the cycle nodes, but since I might want to colour individual segments, I'd also like to draw them separately. How can this be done?

Answer 1

Try and see if this is what you like to obtain:

\documentclass[border=3mm,tikz]{standalone}
\usetikzlibrary{automata}

\begin{document}
   \begin{tikzpicture}
\draw[blue] (60:2) arc (60:360:20mm);
    \node[state,fill=white] (center) at (0,0) {$v_0$};
\foreach \phi in {1,...,6}{
    \node[state,fill=white] (v_\phi) at (360/6 * \phi:2cm) {$v_\phi$};
         \draw[blue] (v_\phi) -- (center);
      }
   \end{tikzpicture}