\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
 
\usepackage{xcolor}
\definecolor{pink}{HTML}{FF00FF}
\definecolor{purple}{HTML}{800080}

\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc,lindenmayersystems,decorations.pathmorphing} 
\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
\tikzstyle{markedCircle}=[line width=1pt,rotate=90,decorate,decoration={snake, segment length=2mm, amplitude=0.4mm}]

\begin{document}
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}

\begin{preview}
\begin{tikzpicture}  [scale=1.2]
  \node (a)[vertex] at (3,1) {a};
  \node (b)[vertex] at (5.5,2.5) {b};
  \node (c)[vertex] at (0.5,3) {c};
  \node (d)[vertex] at (3.5,4.5) {d};
  \node (e)[vertex] at (6,5.5) {e};
  \node (f)[vertex] at (0,6.5) {f};
  \node (g)[vertex] at (3,7) {g};
  \node (h)[vertex] at (4.5,7.5) {h};
  \node (i)[vertex] at (6,7.5) {i};
  \node (j)[vertex] at (1.5,8.5) {j};
  \node (k)[vertex] at (4,9) {k};

  \foreach \from/\to in {a/b,a/b,b/d,b/e,c/f,d/f,d/g,f/g,g/h,h/e,h/i,e/i,f/j,g/j,j/k,k/h,k/i}
    \draw[line width=2pt] (\from) -- (\to);

  \begin{pgfonlayer}{background}
    \draw (a.center) edge[selected edge] (c.center);
    \draw (c.center) edge[selected edge] (f.center);
    \draw (f.center) edge[selected edge] (g.center);
    \draw (g.center) edge[selected edge] (j.center);
    \draw (g.center) edge[selected edge] (h.center);
    \draw (h.center) edge[selected edge] (k.center);
    \draw (g.center) edge[selected edge] (d.center);
    \draw (d.center) edge[selected edge] (b.center);
    \draw (h.center) edge[selected edge] (i.center);
    \draw (h.center) edge[selected edge] (e.center);
  \end{pgfonlayer}

  \draw[color=black!80, markedCircle] (a) -- (c) -- (f) -- (g) -- (d) -- (b) -- (a);
  \draw[color=purple,   markedCircle, fill=purple!10] (f) -- (g) -- (d) -- (f);
  \draw[color=red,      markedCircle] (b) -- (d) -- (g) -- (h) -- (e) -- (b);
  \draw[color=yellow,   markedCircle] (g) -- (h) -- (k) -- (j) -- (g);
  \draw[color=pink,     markedCircle] (f) -- (g) -- (j) -- (f);
  \draw[color=pink,     markedCircle] (f) -- (g) -- (j) -- (f);
  \draw[color=orange,   markedCircle] (h) -- (k) -- (i) -- (h);
  \draw[color=blue,     markedCircle] (h) -- (i) -- (e) -- (h);
\end{tikzpicture}
\end{preview}
\end{document}
