# Making a graph complete

Here's my issue: I created this graph by the following code:

\begin{tikzpicture} \newdimen\R
\R=1.3cm
\draw (0:\R) \foreach \x in {60,120,...,360} {  -- (\x:\R) };
\foreach \x/\l/\p in
{ 60/{$\overline{3}$}/above,
120/{$2$}/above,
180/{$1$}/left,
240/{$3$}/below,
300/{$\overline{2}$}/below,
360/{$\overline{1}$}/right
}
\node[inner sep=1pt,circle,draw,fill,label={\p:\l}] at (\x:\R) {};
\end{tikzpicture}

Now, I would like to add edges between all of the vertices, but I am stuck at how to do that.

\documentclass[tikz, border=20]{standalone}

\begin{document}
\begin{tikzpicture} \newdimen\R
\R=1.3cm
\draw (0:\R) \foreach \x in {60,120,...,360} {  -- (\x:\R) };
\foreach \x/\l/\p in
{ 60/{$\overline{3}$}/above,
120/{$2$}/above,
180/{$1$}/left,
240/{$3$}/below,
300/{$\overline{2}$}/below,
360/{$\overline{1}$}/right
}
\node[inner sep=1pt,circle,draw,fill,label={\p:\l}] at (\x:\R) {};
\foreach \x in {60, 120, ..., 360} {
\draw (\x:\R) -- (\x+120:\R);
\draw (\x:\R) -- (\x+180:\R);
}
\end{tikzpicture}
\end{document}

Just iterate around the circle again but connect every other node and then again but skipping two nodes.

Even if you already accepted Willoughby's answer, I let another solution, maybe more versatile and with a better alignment for the figures.

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}
\def\r{2}
\foreach \c [count=\i from 0] in {
$\overline{1}$,
$\overline{3}$,
$2$,
$1$,
$3$,
$\overline{2}$}
{
\path (0,0) -- (60*\i:\r) node[circle,inner sep=1mm,fill=black](\i){} --++ (60*\i:10pt) node{\c};
}
\foreach \i in {0,...,5}
\foreach \n in {\i,...,5}
\draw (\i.center) -- (\n.center);
\end{tikzpicture}
\end{document}