Circlular graph with arcs joining nodes

circular_graph.tex

\documentclass{article}

\usepackage{tikz}

% These libraries handle the path manipulations
\usetikzlibrary{
  intersections,
  spath3
}

\begin{document}

% Don't use \[...\] just to centre something
\begin{center}
% \tikzstyle is depreciated 
\begin{tikzpicture}[
  every node/.style={
    font=\small,
    draw,
    circle,
    minimum size=.75cm
  },
  r-out/.style={
    draw,
    very thick,
    red,
    -stealth,
  },
  r-btw/.style={
    draw,
    very thick,
    blue,
  },
]

% Declare the nodes and save their outlining paths (needs global) as
% node paths are buried deep in a group
\node[spath/save global=e] (e) at (0:2) {\(1\)};
\node[spath/save global=r] (r) at (90:2) {\(r\)};
\node[spath/save global=r2] (r2) at (180:2) {\(r^2\)};
\node[spath/save global=r3] (r3) at (270:2) {\(r^3\)};
\node[spath/save global=f] (f) at (0:1) {\(f\)};
\node[spath/save global=rf] (rf) at (90:1) {\(r f\)};
\node[spath/save global=r2f] (r2f) at (180:1) {\(r^2 f\)};
\node[spath/save global=r3f] (r3f) at (270:1) {\(r^3 f\)};
% Define the circular paths
\path[spath/save=outer circle] (0,0) circle[radius=2];
\path[spath/save=inner circle] (0,0) circle[radius=1];

% Draw the paths between the inner and outer nodes
\foreach \nd in {r,r2,r3}
{
  \draw[r-btw] (\nd) -- (\nd f);
}
\draw[r-btw] (e) -- (f);

% This set of commands splits the outer and inner circles where they
% meet the node boundaries so that the components inside the
% boundaries can be removed.
\tikzset{
  % Circles have an empty component at the start
  spath/remove empty components=outer circle,
  spath/remove empty components=inner circle,
  % Split at the various intersections
  spath/split at intersections with={outer circle}{e},
  spath/split at intersections with={outer circle}{r},
  spath/split at intersections with={outer circle}{r2},
  spath/split at intersections with={outer circle}{r3},
  spath/split at intersections with={inner circle}{f},
  spath/split at intersections with={inner circle}{rf},
  spath/split at intersections with={inner circle}{r2f},
  spath/split at intersections with={inner circle}{r3f},
  % Remove the components corresponding to the pieces inside the nodes
  spath/remove components={outer circle}{2,4,6,8},
  spath/remove components={inner circle}{2,4,6,8},
  % We want to render these separately to get the arrows
  spath/get components of={outer circle}\ocircleCpts,
  spath/get components of={inner circle}\icircleCpts
}

% Iterate over the components and draw each one
\foreach \cpt in \ocircleCpts {
  \draw[r-out,spath/use=\cpt];
}
\foreach \cpt in \icircleCpts {
  \draw[r-out,spath/use=\cpt];
}

% Just to show that the arcs are circles
\draw (0,0) circle[radius=2] circle[radius=1];

\end{tikzpicture}
\end{center}


\end{document}