\begin{tikzpicture}
  \tikzset{every node/.style={shape=circle,draw,fill=white,inner sep=2pt}}

\node (1) at (-0.5, 0.0) {$1$};
\node (2) at (-4.0, 1.7826024579660036) {$2$};
\node (3) at (-3.0, 1.7826024579660036) {$3$};
\node (5) at (-2.0, 1.7826024579660036) {$5$};
\node (7) at (-1.0, 1.7826024579660036) {$7$};
\node (11) at (0.0, 1.7826024579660036) {$11$};
\node (13) at (1.0, 1.7826024579660036) {$13$};
\node (17) at (2.0, 1.7826024579660036) {$17$};
\node (19) at (3.0, 1.7826024579660036) {$19$};
\node (4) at (-3.0, 3.565204915932007) {$4$};
\node (6) at (-2.0, 3.565204915932007) {$6$};
\node (9) at (-1.0, 3.565204915932007) {$9$};
\node (10) at (0.0, 3.565204915932007) {$10$};
\node (14) at (1.0, 3.565204915932007) {$14$};
\node (15) at (2.0, 3.565204915932007) {$15$};
\node (8) at (-1.5, 5.347807373898011) {$8$};
\node (12) at (-0.5, 5.347807373898011) {$12$};
\node (18) at (0.5, 5.347807373898011) {$18$};
\node (16) at (-0.5, 7.130409831864014) {$16$};

\draw (6) -- (12);
\draw (6) -- (18);
\draw (4) -- (12);
\draw (5) -- (10);
\draw (1) -- (3);
\draw (2) -- (14);
\draw (3) -- (9);
\draw (4) -- (8);
\draw (3) -- (6);
\draw (3) -- (15);
\draw (5) -- (15);
\draw (2) -- (4);
\draw (1) -- (2);
\draw (1) -- (5);
\draw (1) -- (11);
\draw (2) -- (10);
\draw (1) -- (17);
\draw (8) -- (16);
\draw (1) -- (7);
\draw (1) -- (13);
\draw (2) -- (6);
\draw (9) -- (18);
\draw (1) -- (19);
\draw (7) -- (14);

\end{tikzpicture}