سلام
به صورت زیر:
\documentclass[a4paper,12pt]{report}
\usepackage{tikz,amsmath}
\usepackage{xepersian}
\settextfont{Yas}
\tikzstyle{vertex}=[circle, draw, inner sep=0pt, minimum size=4pt]
\newcommand{\vertex}{\node[vertex]}
\tikzstyle{vertexa}=[circle, draw, inner sep=0pt, minimum size=2pt]
\newcommand{\vertexa}{\node[vertexa]}
\begin{document}
%%%
\[\begin{tikzpicture}[scale=1,very thick]
\draw (0,0) circle (2cm);
\vertex[fill] (v1) at (2,0) [] {};
\vertex[fill] (v2) at (1.41,1.41) [] {};
\vertex[fill] (v3) at (0,2) [] {};
\vertex[fill] (v4) at (-1.41,1.41) [] {};
\vertex[fill] (v5) at (-2,0) [] {};
\vertex[fill] (v6) at (-1.41,-1.41) [] {};
\vertex[fill] (v7) at (0,-2) [] {};
\vertex[fill] (v8) at (1.41,-1.41) [] {};
\vertex[fill] (v9) at (0,0) [] {};
\path
(v1) edge (v5)
(v2) edge (v6)
(v3) edge (v7)
(v4) edge (v8);
\end{tikzpicture} \]
%%%%2
\begin{center}
رسم طوقه با:
loop above
\end{center}
\[\begin{tikzpicture} [scale=1,very thick]
\vertexa [fill] (v1) at (0,0) [label=below:$v_{1}$] {};
\vertexa [fill] (v2) at (2,0) [label=right:$v_{2}$] {};
\path
(v1) edge (v2)
(v1) edge [loop above] (v1);
\end{tikzpicture}\]
%%3
\begin{center}
رسم طوقه با: controls
\end{center}\[\begin{tikzpicture} [scale=1,very thick]
\vertexa [fill] (v1) at (0,0) [label=below:$v_{1}$] {};
\vertexa [fill] (v2) at (2,0) [label=right:$v_{2}$] {};
\path
(v1) edge (v2)
(v1) edge (v1);
\draw[->] (0,0) .. controls (-.6,.5)and (.6,.5) .. (0,0);
\end{tikzpicture}\]
\end{document}
خروجی :
