\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,intersections}
\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 (1,1) {};
  \node (b)[vertex] at (2,5) {};
  \node (c)[vertex] at (3,3) {};
  \node (d)[vertex] at (5,4) {};
  \node (e)[vertex] at (3,6) {};
  \node (f)[vertex] at (5,6) {};
  \node (g)[vertex] at (7,6) {};
  \node (h)[vertex] at (7,4) {};
  \node (i)[vertex] at (6,2) {};
  \node (j)[vertex] at (8,7) {};
  \node (k)[vertex] at (9,5) {};
  \node (l)[vertex] at (13,6) {};
  \node (m)[vertex] at (11,7) {};
  \node (n)[vertex] at (15,7) {};
  \node (o)[vertex] at (16,4) {};
  \node (p)[vertex] at (10,2) {};
  \node (q)[vertex] at (13,1) {};
  \node (r)[vertex] at (16,1) {};
  \node (s)[vertex] at (17,4) {};
  \node (t)[vertex] at (19,6) {};
  \node (u)[vertex] at (18,3) {};
  \node (v)[vertex] at (20,2) {};
  \node (w)[vertex] at (15,4) {};

  \foreach \from/\to in {a/c,c/b,c/d,d/f,f/g,g/h,h/d,d/g,h/f,i/k,k/j,k/l,l/m,m/n,n/o,o/t,t/v,v/u,s/r,o/q,q/p,u/t}
    \draw[line width=2pt] (\from) -- (\to);
\end{tikzpicture}
\end{preview}
\end{document}