\begin{tikzpicture}[node distance=4cm, auto]
    \def\V{(0,0),(1,-1),(-1,-1.5),(-1,.5),(-2.5,1),(1,1.5),(.5,3),(-1,2.5),(-2.5,2.5)}
    \def\E{1/2,1/3,3/4,1/4,1/6,2/6,3/2,3/5,5/4/,5/9,9/8,8/7,6/7,4/9,4/7,1/8}
    \def\C{5/4,4/3,3/2,2/1,1/6,6/7,7/8,8/9,9/5}

    \def\G{%
        \foreach \pos[count=\v] in \V \node[vertex] (v-\v) at \pos {};%
        \foreach \u/\v in \E \draw (v-\u) -- (v-\v);%
    }%

    \node[label={below:Graf $G$}] (G) {
        \begin{tikzpicture}
            \G
            \foreach \u/\v in \C \draw[thick, red] (v-\u) -- (v-\v);
        \end{tikzpicture}
    };
    
    \node[label={below:Graf $G_1$}, right of=G, anchor=west] (H) {
        \begin{tikzpicture}
            \G
            \node[vertex, label={below:$v_{101}$}] at (-2,-.5) {};
        \end{tikzpicture}
    };
    
    \draw[->, thick] (G) -- (H);
\end{tikzpicture}