The largest 4-regular graph of diameter 2

See this paper.

\documentclass{article}
\usepackage{tikz}
\pagestyle{empty}

\begin{document}
\begin{center}
\begin{tikzpicture}[style=thick]
\foreach \x in {0,30,...,330}
{
\draw (\x:2cm) circle (2pt) -- (\x+30:2cm);
}
\foreach \x in {0,60,...,300}
{
\draw (\x:2cm) circle (2pt) -- (\x+90:2cm);
}
\foreach \x in {0,30,...,150}
{
\draw (\x:2cm) circle (2pt) -- (\x+180:2cm);
}
\draw (60:0.7cm) circle (2pt) --
(180:0.7cm) circle (2pt) --
(300:0.7cm) circle (2pt) -- (60:0.7cm);
\end{tikzpicture}
\end{center}
\end{document}