How to generalize this graph?

Question

If you know how to answer the question in pstricks I am open to that, but I am doing things in tikz now. I found the below snippet in a tikz manual here: http://pgf.sourceforge.net/pgf_CVS.pdf, on p. 737-8.

\documentclass[11pt]{article}
\usepackage{tikz}
\begin{tikzpicture}
  \foreach \angle in {0,45,...,315}
\node[rectangle,draw=black!50] (\angle) at (\angle:2) {\angle};
  \foreach \from/\to in {0/45,45/90,90/135,135/180,
                         180/225,225/270,270/315,315/0}
\path (\from) edge [->,bend right=22,looseness=0.8] (\to) edge [<-,bend left=22,looseness=0.8] (\to);
\end{tikzpicture}
\end{document}

It makes this:

I want to generalize this to allow for more vertices and edges. Given n vertices, I will be drawing arbitrary walks through the graph, of length n-1 edges. I want the edges to be distinguishable, and also to support labels 1, 2, ...

Help with three things would be great:

1) If I have 6 vertices I need to be able to make 5 loops on a single vertex distinguishable. I don't know how to loop other than above, right, etc.

2) If there are multiple edges going between two vertices (the arrows do NOT have to point all the same way), I want them to bend an even amount between each other.

3) Get a label on the edge (probably literally ON it) which is small and tasteful but also legible.

Because I don't know beforehand how many vertices I will be drawing, or the actual shape of the path, I need to express things rather generally. I can write the code for this if I can get help with the above.

Answer 1

You said that you could write the code for the general recipe given answers to the three specific questions. However, if you want general recipes, TikZ's graph-drawing facilities, especially the various algorithms available, must surely be the way to go.

I do not know this very well - it feels like alien territory - but LuaTeX provides a good deal of power and the documentation and libraries are extensive. If you'll be drawing lots of them, it will be worth your while to invest the time in reading the documentation in the manual.

circular, routing, graphs.standard (for standard graphs such as K_n etc.) should be of particular interest. Note the introduction is in the main bit of the manual and the detail is in the graphs drawing part proper.

Here's a mini-example based on your stated desiderata. (I'm not very clear what these are, so this really means your stated desiderata as best I could fathom them.)

\RequirePackage{luatex85}
\documentclass[border=10pt,multi,tikz]{standalone}
\usetikzlibrary{graphs,graphdrawing,arrows.meta,quotes}
\usegdlibrary{circular}
\begin{document}
\tikz[>=Stealth]{%
  \graph [simple necklace layout, grow'=down, node sep=20mm, nodes=draw, edge quotes center, edge quotes={fill=white, inner sep=1pt, font=\scriptsize}]
  {
    6  ->[bend left, "a"] {5, 4, 3, 2, 1};
    5  ->[bend left, "b"] {6, 4, 3, 2, 1};
    4  ->[bend left, "c"] {6, 5, 3, 2, 1};
    3  ->[bend left, "d"] {6, 4, 5, 2, 1};
    2  ->[bend left, "e"] {6, 4, 3, 5, 1};
    1  ->[bend left, "f"] {6, 4, 3, 2, 5};
  };
}
\end{document}

Obviously, you'd need to create the edges individually if you needed different labels each time - or create a loop, but that would not really be worth it in that case. The subgraph is laying out the nodes.

You could also use e.g. subgraph C_n [n=6, ->], perhaps with necklace routing (libraries: graphs.standard, routing). It really depends on the details of what you are trying to do ...

EDIT

Note that I just provided an example of what's possible. If you use this, obviously you will want to look at the documentation to tweak it to your requirements.

Here are 3 examples using the standard graph drawing elements. A simple counter is used for labelling the edges which is reset between graphs. Use the edge counter style in the argument to edges for the part of the graph where you want paths to be labelled.

\RequirePackage{luatex85}
\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{graphs,graphs.standard,graphdrawing,arrows.meta,quotes}
\usegdlibrary{circular}
\begin{document}
\newcounter{countme}
\setcounter{countme}{0}
\newcommand*\countup{\stepcounter{countme}\thecountme}
\newcommand*\countset{\setcounter{countme}{0}}
\tikzset{%
  edge counter/.style={"\countup"},
}
\tikz[>=Stealth]{%
  \graph [simple necklace layout, grow'=down, node sep=20mm, nodes=draw, edge quotes center, edge quotes={fill=white, inner sep=1pt, font=\scriptsize}]
  {
    subgraph C_n [n=6, -!-];
    { [edges={edge counter, bend left}]
      6  -> 5 ->[loop below] 5 -> 2 -> 6 -> 3;
    }
  };
}
\countset
\tikz[>=Stealth]{%
  \graph [simple necklace layout, grow'=down, node sep=20mm, nodes=draw, edge quotes center, edge quotes={fill=white, inner sep=1pt, font=\scriptsize}]
  {
    subgraph C_n [n=6, -!-];
    { [edges={edge counter, bend left}]
      3  -> 4 ->3 -> 1 -> 2 -> 3;
    };
  };
}
\countset
\tikz[>=Stealth]{%
  \graph [simple necklace layout, grow'=down, node sep=20mm, nodes=draw, edge quotes center, edge quotes={fill=white, inner sep=1pt, font=\scriptsize}]
  {
    subgraph C_n [n=6, -!-];
    { [edges={edge counter, bend right, blue}]
      1  -> {2, 3, 4} ->  5;
    }
  };
}
\end{document}

Note that older installations of TeX will not have luatex85. If your system doesn't have it, just leave it out and it should work fine.

Answer 2

Here is pstricks code for the figure in the O.P.'s post. It uses the pst-poly package: \documentclass[12pt, x11names, border=10pt]{standalone} \usepackage[utf8]{inputenc} \usepackage{fourier} \usepackage{pst-poly} \usepackage{auto-pst-pdf}

\begin{document}

\psset{unit=2cm, dimen=m, arrowinset=0.15}
\begin{pspicture}%
    \newcounter{angle}
    %%%
    \providecommand{\PstPolygonNode}{%
        \psnode(1;\INode){B\INode}{\psframebox[fillstyle=solid, fillcolor=white, linestyle=solid, linecolor=LightSteelBlue3!50]{\theangle}}%
        \addtocounter{angle}{45}}       \psset{ linewidth=0.6pt, linecolor=LightSkyBlue3, arrows=->, arcangle=-20}
    \rput{-22.50}(0,0){\PstOctogon[PolyName =A, linestyle=none]}
    \multido{\ibeg=0+1, \iend=1+1}{7}{\ncarc{B\ibeg}{B\iend}\ncarc{B\iend}{B\ibeg}}
    \everypsbox{\scriptsize}
    \ncarc[shiftB = 15mm]{B7}{B0}\ncarc{B0}{B7}
    \ncarc[angleB=-100]{B4}{B1}\ncput*{a}
    \ncarc[angleA=20, angle=150,arrows=<-]{B6}{B4}\nbput[labelsep=1pt]{b}
    \ncarc[linestyle=dashed,  angleA=-30]{B7}{B3}\ncput*[framesep=1pt, npos=0.4]{c}
    \uput{1.3em}[-150]{-150}(B5){\pscurve[unit=0.35](O)(0.75; -27)(1;0)(0.7; 30)(O)}%% loop
\end{pspicture}

\end{document} 

The angle parameter for \ncarc (= node connection arc) denote the angles made by the arc with the nodes line (angleA for the beginning of the arc, angleB for the end, angle for both).