drawing a regular hexagon

\documentclass[border=1mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
   \newdimen\R
   \R=2.7cm
   \draw (0:\R)
   \foreach \x in {60,120,...,360} {  -- (\x:\R) };
   \foreach \x/\l/\p in
     { 60/{(2,3,1)}/above,
      120/{(2,1,3)}/above,
      180/{(1,2,3)}/left,
      240/{(1,3,2)}/below,
      300/{(3,1,2)}/below,
      360/{(3,2,1)}/right
     }
     \node[inner sep=1pt,circle,draw,fill,label={\p:\l}] at (\x:\R) {};
\end{tikzpicture}
\end{document}

Is this helping you:

\documentclass[10pt]{article}
\usepackage{tikz}

\newlength{\R}\setlength{\R}{2.7cm}

\begin{document}
\begin{tikzpicture}
  %% Try to define a style, to prevent typing
  [inner sep=2mm,
  minicirc/.style={circle,draw=black!20,fill=black!20,thick}]

  %% Now do the circle with nodes
  \node (circ1) at ( 60:\R) [minicirc] {(2,3,1)};
  \node (circ2) at (120:\R) [minicirc] {(2,3,1)};
  \node (circ3) at (180:\R) [minicirc] {(2,3,1)};
  \node (circ4) at (240:\R) [minicirc] {(2,3,1)};
  \node (circ5) at (300:\R) [minicirc] {(2,3,1)};
  \node (circ6) at (360:\R) [minicirc] {(2,3,1)};

  %% Connect those circs
  \draw [thick] (circ1) to (circ2) to (circ3) 
  to (circ4) to (circ5) to (circ6) to (circ1);

\end{tikzpicture}
\end{document}

(This was my first attempt on TikZ :-) Thank you)

This is the result:

I've tried this first with your loop. But it seems, as if the names of the elements ("circ1", ...) are local to the loop and hence can't be addressed from outside the loop. So I did it manually without loop.

If the color of the circles doesn't suit you, you can easily change its definition in the style. Maybe you'll have to set the color of the text to be white ...