\documentclass[10pt,letterpaper]{article}
\usepackage{tikz}
\begin{document}
	\begin{tikzpicture}[state/.style={circle,fill=black,draw,inner sep=0pt,minimum size=0.2cm}]
		\node[state] (s) at (0,0)[label={[label distance=0.2cm,anchor=base]180:$s_{1}$}] {};
		\node[state] (s2) at (0,1)[label={[label distance=0.2cm,anchor=base]180:$s_{2}$}] {};
		\draw (s) edge [->,out=315,in=45,looseness=28] node[above] {$e$} (s);
		\draw[->] (s) -- (s2);
	\end{tikzpicture}

	\begin{tikzpicture}[state/.style={circle,fill=black,draw,inner sep=0pt,minimum size=0.2cm}]
		\node[state] (s) at (0,0)[label={[label distance=0.2cm,anchor=base]180:$s_{1}$}] {};
		\node[state] (s2) at (0,1)[label={[label distance=0.2cm,anchor=base]180:$s_{2}$}] {};
		\draw (s) edge [->,out=315,in=0,looseness=28] node[above] {$e$} (s);
		\draw[->] (s) -- (s2);
	\end{tikzpicture}
\end{document}
