how do I create a complete graph in tikz?

Question

I have the following code that I created:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[->]

  \node[label=west:$s$,circle,fill,inner sep=1.5pt] (n0) at (-1,1) {};
  \node[label=west:$e_1$,circle,fill,inner sep=1.5pt] (n3) at (0,2) {};
  \node[label=east:$e_2$,circle,fill,inner sep=1.5pt] (n4) at (2,2) {};
  \node[label=west:$e_3$,circle,fill,inner sep=1.5pt] (n1) at (0,0) {};
  \node[label=east:$e_4$,circle,fill,inner sep=1.5pt] (n2) at (2,0) {};
  \node[label=north:$e_5$,circle,fill,inner sep=1.5pt] (n5) at (1,1) {};
  \node[label=south:$e_6$,circle,fill,inner sep=1.5pt] (n6) at (1,0) {};
  \node[label=west:$e$,circle,fill,inner sep=1.5pt] (n7) at (3,1) {};

\path
(n1) edge [bend right=60] node [swap] {} (n2);

\end{tikzpicture}

\end{document}

I want to create edges, just like the bended ones between all $e_i$ (complete directed graph with edges going both ways) and between $s -> e_i$ and $e_i -> e$.

I could do it manually, but it seems very taxing, especially since the graph could become larger. I would also have to bend each edge in the right way.

Is there some package/magic tikz option that would allow me to create a complete subgraph over $e_i$ and add edges between $s$ to all $e_i$ and between all $e_i$ to $e$?

Answer 1

Is this what you're trying to accomplish?

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}

\begin{document}

\begin{tikzpicture}[-{Stealth[scale=1.25]},my node style/.style={circle,fill,inner sep=1.5pt}]

  \node[label=west:$s$,my node style]    (n0) at (-1,1) {};
  \node[label=west:$e_1$,my node style]  (n3) at (0,2)  {};
  \node[label=east:$e_2$,my node style]  (n4) at (2,2)  {};
  \node[label=west:$e_3$,my node style]  (n1) at (0,0)  {};
  \node[label=east:$e_4$,my node style]  (n2) at (2,0)  {};
  \node[label=north:$e_5$,my node style] (n5) at (1,1)  {};
  \node[label=south:$e_6$,my node style] (n6) at (1,0)  {};
  \node[label=west:$e$,my node style]    (n7) at (3,1)  {};

  \let\myp\relax
  \foreach \myc in {1,2,4,3,1}
  {
    \ifx\myp\relax
    \else
      \path (n\myp) edge [bend right=50] node [swap] {} (n\myc);
      \path (n\myc) edge [bend right=20] node [swap] {} (n\myp);
    \fi
    \xdef\myp{\myc}
  }
\end{tikzpicture}

\end{document}

It seems that some kind of tweaking is going to be necessary to avoid getting a rat's nest. Here I should an approach that might suit you. (Note I changed your names for the nodes because, frankly, I found your names rather confusing.)

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}

\begin{document}

\begin{tikzpicture}[-{Stealth[scale=1.25]},my node style/.style={circle,fill,inner sep=1.5pt}]

  \node[label=west:$s$,my node style]    (s) at (-1,1) {};
  \node[label=west:$e_1$,my node style]  (e1) at (0,2)  {};
  \node[label=east:$e_2$,my node style]  (e2) at (2,2)  {};
  \node[label=west:$e_3$,my node style]  (e3) at (0,0)  {};
  \node[label=east:$e_4$,my node style]  (e4) at (2,0)  {};
  \node[label=north:$e_5$,my node style] (e5) at (1,1)  {};
  \node[label=south:$e_6$,my node style] (e6) at (1,0)  {};
  \node[label=west:$e$,my node style]    (e) at (3,1)  {};

  \let\myp\relax
  \foreach \myc in {1,2,4,3,1}
  {
    \ifx\myp\relax
    \else
      \path (e\myp) edge [bend right=20] node [swap] {} (e\myc);
      \path (e\myc) edge [bend right=30] node [swap] {} (e\myp);
    \fi
    \xdef\myp{\myc}
  }


  \foreach \myc/\myout/\myin/\mylooseness in {1/120/130/2,
                                              2/135/130/2,   
                                              3/250/250/1.5,   
                                              4/210/250/2,    
                                              5/0/180/0,    
                                              6/230/230/2}
  {
      \path[red] (s) edge [out=\myout,in=\myin,looseness=\mylooseness] node [swap] {} (e\myc);
  }



\end{tikzpicture}

\end{document}