\documentclass[convert=true, tikz]{standalone}

\begin{document}
\begin{tikzpicture}
  \node (1) at (0,0) [shape=circle, draw] {1};
  \node (2) at (2,0) [shape=circle, draw] {2};
  \node (3) at (4,0) [shape=circle, draw] {3};
  \node (4) at (0,2) [shape=circle, draw] {4};
  \node (5) at (2,2) [shape=circle, draw] {5};
  \node (6) at (4,2) [shape=circle, draw] {6};

  \draw (2) -- (3) -- (6) -- (5) -- (2) -- (6);
  \draw (3) -- (5);
  \draw [thick] (3,1) circle [radius=1.85];
  \node (s1) at (5.1,1) {$S_1$};

  \draw (1) -- (2) -- (4) -- (1);
  \draw [thick, rounded corners] (-0.5,-0.5)
  -- (2.5,-0.5)
  -- (2.5,0.25)
  -- (0.25,2.5)
  -- (-0.5,2.5)
  -- cycle;
  \node (s2) at (-0.75,1) {$S_2$};

  \draw (4) -- (5);
  \draw [thick] (1,2) circle [x radius=1.618, y radius=0.618];
  \node (s3) at (1,2.9) {$S_3$};
\end{tikzpicture}
\end{document}