\begin{tikzpicture}
	\foreach \pos/\w [count=\xi] in { (1, 3)/2, (2.5,4)/1, (0, 2)/4, (3, 2)/5, (-1, 5)/2, (1, 6)/3 } {
		\node[vertex] (v-\xi) at \pos {$\xi$};
        \node[above right=-1mm of v-\xi, weight] {$\w$};
    }
	
    \begin{pgfonlayer}{background}
	\foreach \v/\u in {1/4,1/5,1/2,1/3,3/4,3/5,5/2,2/4,1/6,5/6,2/6}
		\draw (v-\v) edge (v-\u);
    \end{pgfonlayer}
\end{tikzpicture}