% A complete graph
% Author: Quintin Jean-Noël
% <http://moais.imag.fr/membres/jean-noel.quintin/>
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
\usepackage{tikz}
\usetikzlibrary[topaths]


\begin{document}
    \newcommand\n{5}
    \begin{tikzpicture}
        \node[vertex] (a) at (3,6) {};
        \node[vertex] (b) at (2,4) {};
        \node[vertex] (c) at (4,4) {};
        \node[vertex] (d) at (1,2) {};
        \node[vertex] (e) at (2,2) {};
        \node[vertex] (f) at (3,2) {};
        \node[vertex] (g) at (4,2) {};
        \node[vertex] (h) at (0,0) {};
        \node[vertex] (i) at (2,0) {};
        \node[vertex] (j) at (3,0) {};
        \node[vertex] (k) at (5,0) {};

        \draw[red] (a) -- (b);
        \draw[red] (a) -- (c);
        \draw[red] (b) -- (d);
        \draw[red] (b) -- (e);
        \draw[red] (b) -- (f);
        \draw[red] (d) -- (h);
        \draw[red] (d) -- (i);
        \draw[red] (c) -- (g);
        \draw (g) -- (j);
        \draw (g) -- (k);
    \end{tikzpicture}
\end{document}
