\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
 
\usepackage{tikz}
\usetikzlibrary{arrows,positioning, calc} 
\tikzstyle{vertex}=[draw,fill=black!15,circle,minimum size=20pt,inner sep=0pt]
\tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]

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

\begin{preview}
\begin{tikzpicture}  [scale=1.2]
  \node (a)[vertex] at (0,2) {a};
  \node (b)[vertex] at (1,1) {b};
  \node (c)[vertex] at (3,2) {c};
  \node (d)[vertex] at (4,1) {d};
  \node (e)[vertex] at (2,0) {e};
  \node (f)[vertex] at (1,3) {f};
  \node (g)[vertex] at (5,3) {g};
  \node (h)[vertex] at (0,1) {h};

  \foreach \from/\to in {a/f,f/g,h/b,b/c,c/d,d/e,e/b,f/c}
    \draw (\from) -- (\to);

  \begin{pgfonlayer}{background}
    \draw (b.center) edge[selected edge] (c.center);
    \draw (c.center) edge[selected edge] (d.center);
    \draw (d.center) edge[selected edge] (e.center);
    \draw (e.center) edge[selected edge] (b.center);
  \end{pgfonlayer}
\end{tikzpicture}
\end{preview}
\end{document}
