\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows,positioning} 
\tikzset{
    %Define standard arrow tip
    >=stealth',
    % Define arrow style
    pil/.style={->,thick}
}

\begin{document}
  \begin{tikzpicture}
      \node (a)[vertex] at (0,8) {$a$};
      \node (b)[vertex] at (0,4) {$b$};
      \node (c)[vertex] at (0,0) {$c$};
      \node (d)[vertex] at (4,4) {$d$};

      \foreach \from/\to/\pos in {a/b/20,a/b/-20,a/d/0,b/c/20,b/c/-20,b/d/0,c/d/0}
        \draw[line width=2pt] (\from) to [bend left=\pos] (\to);
  \end{tikzpicture}
\end{document}