I have this code:
\documentclass{minimal}
\usepackage{tikz}
\usepackage{tkz-graph}
\usetikzlibrary{external,backgrounds}
%\expandafter\tikzexternalize[]
\begin{document}
\begin{tikzpicture}[
yscale=.75,
VertexStyle/.style={} % removes white fill from vertices
]
\Vertex[L=$1$]{1}
\NOEA[L=$2$](1){2}
\NOEA[L=$3$](2){3}
\NOEA[L=$4$](3){4}
\NOEA[L=$5$](4){5}
\SOEA[L=$2$](1){22}
\NOEA[L=$3$](22){23}
\NOEA[L=$4$](23){24}
\NOEA[L=$5$](24){25}
\NOEA[L=$6$](25){26}
\SOEA[L=$3$](22){33}
\NOEA[L=$4$](33){34}
\NOEA[L=$5$](34){35}
\NOEA[L=$6$](35){36}
\NOEA[L=$7$](36){37}
\Edges(1,2,3,4,5)
\Edges(22,23,24,25,26)
\Edges(33,34,35,36,37)
\Edges(1,22,33)
\Edges(2,23,34)
\Edges(3,24,35)
\Edges(4,25,36)
\Edges(5,26,37)
\begin{scope}[
on background layer, % everything in the environment is drawn behind the vertices
highlight/.style={rounded corners=1em,line width=1.5em,black,opacity=0.2,cap=round},
whiten/.style={white,cap=round,line width=2em},
highlightfill/.style={fill,line width=1.5em,rounded corners=1em,black,opacity=0.2,cap=round}
]
% order is important !!!
\draw [highlightfill] (2.center) -- (4.center) -- (25.center) -- (26.center) -- (37.center) -- (33.center) -- (1.center) -- (2.center);
\end{scope}
\end{tikzpicture}
\end{document}
producing the following:
Is it possible to have the outline and filling non-overlapping? Or extend the filling in a manner that its outer shape comes close to the depicted one?
PS: You could also have a look at TiKz and tikz-grph background of Graph.



black!20in place ofblack,opacity=0.2. The fill and outline will still overlap, but you won't be able to see one through the other. – Emma Oct 18 '16 at 17:55