\newcommand{\point}[4]{
  \node [label=#3:#4] (#1) at #2 {};
}

\newcommand{\wpath}[3]{
  \draw (#1) -- (#2) node [midway, above, sloped] (Tx#1#2) {{\tiny $#3$}};
}

\begin{tikzpicture}[]
  \begin{scope}[every node/.style={fill=black, shape=circle, inner sep=1pt}]
    \point{1}{(0,1)}{left}{$v_1$}
    \point{2}{(1,2)}{above}{$v_2$}
    \point{3}{(1,0)}{below}{$v_3$}

    \point{4}{(3,2)}{above left}{$v_4$}
    \point{5}{(3,0)}{below right}{$v_5$}

    \point{6}{(5,2)}{above left}{$v_6$}
    \point{7}{(5,0)}{above left}{$v_7$}
    \point{8}{(6,1)}{above right}{$v_8$}
  \end{scope}
  
  \wpath{1}{3}{1}
  \wpath{2}{3}{2}
  \wpath{7}{8}{2}
  \wpath{3}{5}{3}
  \wpath{4}{5}{4}
  \wpath{6}{8}{5}
  \wpath{5}{6}{6}
  \wpath{6}{7}{7}
  \wpath{5}{7}{8}
  \wpath{4}{6}{9}
  \wpath{2}{5}{10}
  \wpath{2}{4}{11}
  \wpath{1}{2}{12}

\end{tikzpicture}