Drawing partial NFAs with TikZ/PGF

Question

I've started using LaTeX recently, and I'm trying to draw a few partial NFAs for an article; I have little to no experience with TikZ, so forgive me for asking something that is probably trivial.

I'm trying to draw images like these:

(Those came from here.)

So far I could position the nodes:

\documentclass{article}
\usepackage{tikz}
\begin{document}
  \pagestyle{empty}
  Partial NFA example:

  \begin{tikzpicture}[shorten >=1pt,->]
    \tikzstyle{state}=[circle,draw=black,thick]
    \tikzstyle{block}=[rectangle,draw=black,thick,minimum width=25pt]

    \node[state] (s) at (1,1) { };
    \node[block] (e) at (5,2) {\texttt{e}};
    \node[] (x) at (4,0) { };

    \draw (0,0) -- (s); % Start
    \draw (s) edge[bend left=30] (e);
    \draw (e) edge[bend left=30] (s);
    \draw (s) edge[bend right=30] (x);
  \end{tikzpicture}
\end{document}

But I couldn't get even close to what I want. I have no idea how to make the arrows properly.

Could anyone give me some help?

Answer 1

Not a full answer yet, but this should lead you into the right direction ... For details on how the code works, please have a look at the comments in the code, which only contains minor changes to your provided code.

\documentclass[border=2mm]{standalone}
\usepackage{tikz}
    \usetikzlibrary{
        arrows.meta,
    }
\begin{document}
\begin{tikzpicture}

    \tikzstyle{state}=[circle,draw=black,thick]
    \tikzstyle{block}=[rectangle,draw=black,thick,minimum width=25pt]

    \node [state] (s) at (1,1) { };
    \node [block] (e) at (5,2) {\texttt{e}};
    \node []      (x) at (4,0) { };

    \begin{scope}[
        ->,
        shorten >=1pt,
        % draw corners rounded
        rounded corners=2mm,
    ]
        % connect the nodes vertical and horizontal lines (`|-')
        % (if you need to draw first horizontal and then vertical lines
        %  use `-|' instead)
        \draw (0,0) |- (s); % Start
        \draw (s) |- (e);
        \draw (e) |-  (s);
        \draw (s) |- (x);

        \draw [draw=white,{To[black]}-,shorten <=1pt] (e.east) -- +(5pt,0);
    \end{scope}
\end{tikzpicture}
\end{document}