\begin{tikzpicture}[graph vertex/.style={draw, circle, minimum size=0.5cm}]
\node[graph vertex, third] (v1) at (.50, 5.00) {1};
\node[graph vertex, second] (v2) at (2.50, 5.00) {2};
\node[graph vertex, fourth] (v3) at (5.00, 5.00) {3};
\node[graph vertex, third] (v4) at (4.00, 4.15) {4};
\node[graph vertex, fourth] (v5) at (1.00, 3.50) {5};
\node[graph vertex, third] (v6) at (5.50, 3.50) {6};
\node[graph vertex, first] (v7) at (2.80, 3.00) {7};
\node[graph vertex, third] (v8) at (1.40, 2.25) {8};
\node[graph vertex, second] (v9) at (4.00, 2.55) {9};
\node[graph vertex, third] (v10) at (5.50, 2.20) {10};
\node[graph vertex, second] (v11) at (2.90, 1.50) {11};
\node[graph vertex, third] (v12) at (4.20, 1.25) {12};
\node[graph vertex, fourth] (v13) at (5.50, 1.00) {13};
\node[graph vertex, fourth] (v14) at (1.00, .80) {14};
\node[graph vertex, third] (v15) at (2.80, .10) {15};
\node[graph vertex, fourth] (v16) at (4.50, .07) {16};

\graph {
  (v1) -- (v2),
  (v2) -- (v4),
  (v3) -- (v6),
  (v3) -- (v4),
  (v4) -- (v9),
  (v2) -- (v7),
  (v7) -- (v9),
  (v9) -- (v6),
  (v7) -- (v11),
  (v9) -- (v11),
  (v9) -- (v10),
  (v9) -- (v11),
  (v10) -- (v11),
  (v11) -- (v12),
  (v12) -- (v13),
  (v13) -- (v16),
  (v16) -- (v15),
  (v8) -- (v11),
  (v5) -- (v8),
  (v8) -- (v14),
  (v14) --[bend left] (v5),
  (v4) -- (v6),
  (v11) -- (v15),
  (v10) -- (v13),
  (v6) -- (v10)
};
\end{tikzpicture}