Making an image out of a picture of a Cayley diagram

Question

I'm trying to convert this picture of a Cayley graph into latex, but I'm not sure how to create my own image. Is there any easy-to-use software that allows users to make Cayley diagrams in latex?

Thanks.

Answer 1

Here's a version of your Cayley diagram done with Metapost and luamplib.

You need to compile the source below with lualatex in order to use the built in Metapost engine. If you are using a different LaTeX engine, you can easily adapt this solution to work with plain Metapost. Follow the links above for details.

Whether this is "easy-to-use" of course depends on your background and skills. The advantages are that you get a very precise result. The only tricky bit of this program is the function to draw the connections, but there's nothing in there that's not explained in the various Metapost tutorials and manuals linked above.

\documentclass[border=5mm]{standalone}
\usepackage{unicode-math}
\setmathfont{TeX Gyre Schola Math}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
    vardef connect(expr a,b, txt, shade) = 
      save p; path p; p = a { (b-a) rotated 24 } .. b;
      save m; numeric m; m = arctime (arclength(p)+ahlength)/2 of p;
      drawarrow subpath(0,m) of p cutbefore fullcircle scaled 20 shifted a withcolor shade;
      draw      subpath(m,1) of p cutafter  fullcircle scaled 20 shifted b withcolor shade;
      label(txt, point m of p shifted (unitvector(direction m of p) rotated 90 scaled 8)) withcolor shade;
    enddef;

    beginfig(1);
       path inside, outside;
       inside = reverse fullcircle scaled 100 rotated 90;
       z0 = point 0   of inside;
       z1 = point 1.6 of inside;
       z2 = point 3.2 of inside;
       z3 = point 4.8 of inside;
       z4 = point 6.4 of inside;

       outside = inside scaled 1.8;
       z10 = point 0   of outside;
       z11 = point 1.6 of outside;
       z12 = point 3.2 of outside;
       z13 = point 4.8 of outside;
       z14 = point 6.4 of outside;

       label("$e$"  , z0);
       label("$r_1$", z1); 
       label("$r_2$", z2); 
       label("$r_3$", z3); 
       label("$r_4$", z4); 

       label("$d_1$", z10);
       label("$d_4$", z11); 
       label("$d_2$", z12); 
       label("$d_5$", z13); 
       label("$d_3$", z14); 

       connect(z0,z1, "$r$", 1/2 red+blue);
       connect(z1,z2, "$r$", 1/2 red+blue);
       connect(z2,z3, "$r$", 1/2 red+blue);
       connect(z3,z4, "$r$", 1/2 red+blue);
       connect(z4,z0, "$r$", 1/2 red+blue);

       connect(z10,z11, "$r$", 1/2 red+blue);
       connect(z11,z12, "$r$", 1/2 red+blue);
       connect(z12,z13, "$r$", 1/2 red+blue);
       connect(z13,z14, "$r$", 1/2 red+blue);
       connect(z14,z10, "$r$", 1/2 red+blue);

       connect(z0,z10, "$d$", 2/3 blue); connect(z10,z0, "$d$", 2/3 blue);
       connect(z1,z11, "$d$", 2/3 blue); connect(z11,z1, "$d$", 2/3 blue);
       connect(z2,z12, "$d$", 2/3 blue); connect(z12,z2, "$d$", 2/3 blue);
       connect(z3,z13, "$d$", 2/3 blue); connect(z13,z3, "$d$", 2/3 blue);
       connect(z4,z14, "$d$", 2/3 blue); connect(z14,z4, "$d$", 2/3 blue);

    endfig;
\end{mplibcode}
\end{document}

Answer 2

Probably not perfect, but a step in the right direction:

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{decorations.markings,arrows.meta}
\begin{document}
\begin{tikzpicture}[mid arrow/.style={postaction={
  decoration={markings, mark=at position 0.5 with {\arrow{Triangle}}},
  decorate}},looseness=0.5]
\foreach \i [count=\j, count=\r from 0] in {1, 4, 2, 5, 3}{
   \node (d\j) at (90+72-\j*72:3) {$d_\i$};
   \node (r\j) at (90+72-\j*72:3/2) {$\ifnum\i=1e\else r_\r\fi$};
}
\foreach \i [evaluate={\j=int(mod(\i, 5)+1);}] in {1,...,5}{
  \draw [purple, mid arrow] (d\i) to [bend left] node [auto] {$r_1$} (d\j);
  \draw [purple, mid arrow] (r\i) to [bend left] node [auto] {$r_1$} (r\j);
  \draw [blue, mid arrow]   (r\i) to [bend left] node [auto] {$d_1$} (d\i);
  \draw [blue, mid arrow]   (d\i) to [bend left] node [auto] {$d_1$} (r\i);
} 
\end{tikzpicture}
\end{document}