A complete graph on 5 vertices with coloured edges

Question

I was unable to create a complete graph on 5 vertices with edges coloured red and blue in Latex. The picture of such graph is below. I would be very grateful for help!

Answer 1

• Use polar coordinates (angle:distance). For a pentagon, the angles differ by 360/5 = 72 degrees. Since one node is supposed to be at angle 90 (north), the angles are computed from there as 18, 90, 162, 234, and 306 degrees.
• Lookup the \foreach loop as well as the \draw and \node commands in the TikZ manual.

\documentclass[border=2pt]{standalone}
\usepackage{tikz}
\begin{document}
\newcommand\size{1}% distance of nodes from center
\begin{tikzpicture}
  \draw[thick,red]  (18:\size) \foreach \a in {90,162,234,306} { -- (\a:\size) } -- cycle;
  \draw[thick,blue] (18:\size) \foreach \a in {162,306,90,234} { -- (\a:\size) } -- cycle;
  \foreach \a in {18,90,162,234,306} { \node[black,fill=black,circle,inner sep=2pt] at (\a:\size){}; }
\end{tikzpicture}
\end{document}

Answer 2

Very easy using MetaPost:

\documentclass{standalone}
\usepackage[latex,shellescape]{gmp}
\begin{document}
\begin{mpost}[name=nice]
numeric u; u := 3cm;
for i = 1 upto 5:
    for j = 1 upto i:
        if i <> j:
            draw (u*dir (72i+18)) -- (u*dir(72j+18)) withcolor
            if (abs(i-j) = 1) or (abs(i-j) = 4):
                red
            else:
                blue
            fi
            withpen currentpen scaled 4;
        fi
    endfor
endfor
for i = 1 upto 5: drawdot (u*dir (72i+18)) withpen currentpen scaled 20; endfor
\end{mpost}%
\usempost{nice}%
\end{document}

Answer 3

An alternative (for exercise), with using of the regular polygon shape and double loop:

\documentclass[tikz, margin=3.141592]{standalone}
\usetikzlibrary{shapes.geometric}

\begin{document}
    \begin{tikzpicture}[
dot/.style = {circle, fill=black, inner sep=2pt, outer sep=0pt}
                    ]
\node (n)   [regular polygon, 
             regular polygon sides=5, minimum size=22mm,
             draw=red, thick]  {};
\foreach \i in {1,2,...,5} 
{     
    \foreach \j [evaluate=\j as \k using int(\i+\j)] in {2,3}
    {
    \ifnum\k<6
    \draw[thick,blue]   (n.corner \i) -- (n.corner \k);
    \fi
    }
\node [dot] at (n.corner \i) {};
}
    \end{tikzpicture}
\end{document}

Answer 4

Graphs can be produced with the graphs library.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{graphs,graphs.standard}
\begin{document}
\begin{tikzpicture}
\graph [nodes={circle,inner sep=1pt,fill},radius=1.75cm, 
    clockwise, empty nodes,n=5] { 
    subgraph I_n [clique,edge=blue]; 
    subgraph C_n [edge={red,semithick}]; ,
    };
\end{tikzpicture}
\end{document}