% whole medial graph: n=20 seed=72 source=9 recognised treads=[2] |M(G)|=54
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\\[-0.25ex]
{\scriptsize source graph $G$}
\\[1.0ex]
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\node[elbl] at (0.217,-0.241) [yshift=-4.8pt] {$4\!{-}\!6$};
\node[elbl] at (0.245,-0.247) [yshift=-4.8pt] {$4\!{-}\!7$};
\node[elbl] at (0.216,-0.226) [yshift=-4.8pt] {$4\!{-}\!8$};
\node[elbl] at (-0.079,-0.351) [yshift=-4.8pt] {$5\!{-}\!9$};
\node[elbl] at (0.263,-0.286) [yshift=-4.8pt] {$6\!{-}\!7$};
\node[elbl] at (0.233,-0.265) [yshift=-4.8pt] {$6\!{-}\!8$};
\node[elbl] at (0.262,-0.270) [yshift=-4.8pt] {$7\!{-}\!8$};
\node[elbl] at (0.325,-0.387) [yshift=-4.8pt] {$10\!{-}\!2$};
\node[elbl] at (0.089,-0.299) [yshift=-4.8pt] {$10\!{-}\!3$};
\node[elbl] at (0.081,-0.348) [yshift=-4.8pt] {$10\!{-}\!5$};
\node[elbl] at (0.107,-0.329) [yshift=-4.8pt] {$10\!{-}\!14$};
\node[elbl] at (0.377,-0.378) [yshift=-4.8pt] {$11\!{-}\!2$};
\node[elbl] at (0.140,-0.290) [yshift=-4.8pt] {$11\!{-}\!3$};
\node[elbl] at (0.244,-0.302) [yshift=-4.8pt] {$11\!{-}\!6$};
\node[elbl] at (-0.096,-0.301) [yshift=-4.8pt] {$12\!{-}\!3$};
\node[elbl] at (-0.194,-0.347) [yshift=-4.8pt] {$12\!{-}\!9$};
\node[elbl] at (-0.224,-0.345) [yshift=-4.8pt] {$12\!{-}\!19$};
\node[elbl] at (0.210,-0.222) [yshift=-4.8pt] {$13\!{-}\!4$};
\node[elbl] at (0.227,-0.260) [yshift=-4.8pt] {$13\!{-}\!6$};
\node[elbl] at (0.227,-0.245) [yshift=-4.8pt] {$13\!{-}\!8$};
\node[elbl] at (0.219,-0.236) [yshift=-4.8pt] {$13\!{-}\!16$};
\node[elbl] at (0.045,-0.287) [yshift=-4.8pt] {$14\!{-}\!3$};
\node[elbl] at (0.038,-0.336) [yshift=-4.8pt] {$14\!{-}\!5$};
\node[elbl] at (0.087,-0.250) [yshift=-4.8pt] {$15\!{-}\!3$};
\node[elbl] at (0.173,-0.223) [yshift=-4.8pt] {$15\!{-}\!4$};
\node[elbl] at (0.190,-0.262) [yshift=-4.8pt] {$15\!{-}\!6$};
\node[elbl] at (0.135,-0.239) [yshift=-4.8pt] {$15\!{-}\!18$};
\node[elbl] at (0.209,-0.217) [yshift=-4.8pt] {$16\!{-}\!4$};
\node[elbl] at (0.225,-0.240) [yshift=-4.8pt] {$16\!{-}\!8$};
\node[elbl] at (-0.065,-0.171) [yshift=-4.8pt] {$17\!{-}\!3$};
\node[elbl] at (0.076,-0.246) [yshift=-4.8pt] {$18\!{-}\!3$};
\node[elbl] at (0.162,-0.218) [yshift=-4.8pt] {$18\!{-}\!4$};
\node[elbl] at (-0.102,-0.301) [yshift=-4.8pt] {$19\!{-}\!3$};
\node[dlbl] at (0.350,-0.318) [yshift=5.0pt] {6};
\node[dlbl] at (0.367,-0.357) [yshift=5.0pt] {7};
\node[dlbl] at (0.217,-0.241) [yshift=5.0pt] {0};
\node[dlbl] at (0.262,-0.270) [yshift=5.0pt] {2,3};
\node[dlbl] at (0.227,-0.245) [yshift=5.0pt] {1};
\node[dlbl] at (0.219,-0.236) [yshift=5.0pt] {5};
\node[dlbl] at (0.225,-0.240) [yshift=5.0pt] {4};
\draw[cut] (0.241,-0.204)--(0.180,-0.239);
\node[cutlbl] at (0.137,-0.263) {cut 1};
\draw[cut] (0.256,-0.320)--(0.269,-0.251);
\node[cutlbl] at (0.279,-0.203) {cut 2};
\end{tikzpicture}
\\[-0.25ex]
{\scriptsize medial graph $M(G)$ at edge midpoints}
\end{tabular}