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}
Best Answer
Here's a little example: two "outer" nodes, each one containing a graph (formed with "inner" nodes) and some edges and arrows connecting outer nodes to outer nodes, and inner nodes from one graph to inner nodes of the other; the
remember picture
option lets you access inner and outer nodes at any time: