如何绘制图中的自环和平行边（在投影仪中工作）

Question 1

通过使用automata库（类似于 @js bibra 在他的回答：+1），对于箭头，不是使用平行箭头而是使用弯曲的箭头，从序言中删除了由（，）arrows.meta加载的包，在演示中没有意义（）或与最近的 LaTeX 默认功能（）相关：beamerxcoloramsmathsetspace[utf]{inputenc}

\documentclass[12pt,fleqn]{beamer}
\usetheme{AnnArbor}
\usecolortheme{beaver}
\usefonttheme{professionalfonts} % using non standard fonts for beamer
\usefonttheme{serif} % default family is serif
\addtobeamertemplate{frametitle}{}{\vspace{-0.4em}} % decrease
%\usepackage{setspace}
%\usepackage{amsmath}
%\usepackage[utf8]{inputenc}
\usepackage{pgfplots}   % it load tikz and pgf too
\pgfplotsset{compat=1.17}

\usepackage{mathrsfs}
\usetikzlibrary{arrows.meta, automata,
                positioning,
                shadows}
\begin{document}
\begin{frame}
\begin{center}
    \begin{tikzpicture}[
      node distance = 22mm and 22mm,
state/.append style = {circle, draw=orange, fill=orange, 
                       minimum size=1.2em},
every edge/.style = {draw, -Stealth, semithick}
                        ] 
    \begin{scope}[nodes=state]
\node (n1)  {$v_1$};
\node (n2)  [right=of n1]   {$v_2$};
\node (n3)  [below=of n2]   {$v_3$};
\node (n4)  [left =of n3]   {$v_4$};
    \end{scope}
\path   (n3) edge  (n4)
        (n4) edge  (n1)
        (n1) edge [loop above,looseness=15]  (n1)
        (n1) edge  (n2)
        (n2) edge [bend left=15] (n3)
        (n3) edge [bend left=15] (n2)
        ;
    \end{tikzpicture}
\end{center}
\end{frame}
\end{document}

Answer

通过使用automata库（类似于 @js bibra 在他的回答：+1），对于箭头，不是使用平行箭头而是使用弯曲的箭头，从序言中删除了由（，）arrows.meta加载的包，在演示中没有意义（）或与最近的 LaTeX 默认功能（）相关：beamerxcoloramsmathsetspace[utf]{inputenc}

\documentclass[12pt,fleqn]{beamer}
\usetheme{AnnArbor}
\usecolortheme{beaver}
\usefonttheme{professionalfonts} % using non standard fonts for beamer
\usefonttheme{serif} % default family is serif
\addtobeamertemplate{frametitle}{}{\vspace{-0.4em}} % decrease
%\usepackage{setspace}
%\usepackage{amsmath}
%\usepackage[utf8]{inputenc}
\usepackage{pgfplots}   % it load tikz and pgf too
\pgfplotsset{compat=1.17}

\usepackage{mathrsfs}
\usetikzlibrary{arrows.meta, automata,
                positioning,
                shadows}
\begin{document}
\begin{frame}
\begin{center}
    \begin{tikzpicture}[
      node distance = 22mm and 22mm,
state/.append style = {circle, draw=orange, fill=orange, 
                       minimum size=1.2em},
every edge/.style = {draw, -Stealth, semithick}
                        ] 
    \begin{scope}[nodes=state]
\node (n1)  {$v_1$};
\node (n2)  [right=of n1]   {$v_2$};
\node (n3)  [below=of n2]   {$v_3$};
\node (n4)  [left =of n3]   {$v_4$};
    \end{scope}
\path   (n3) edge  (n4)
        (n4) edge  (n1)
        (n1) edge [loop above,looseness=15]  (n1)
        (n1) edge  (n2)
        (n2) edge [bend left=15] (n3)
        (n3) edge [bend left=15] (n2)
        ;
    \end{tikzpicture}
\end{center}
\end{frame}
\end{document}

Question 2

添加以下行

\path
(v1) edge [->,loop above] node {} (v1);

就在 \endtikzpicture 之前

编辑 - 可能感兴趣并且可以编辑/修改的替代解决方案

\documentclass[12pt,fleqn]{beamer} 
\usetheme{AnnArbor} 
\usepackage{setspace} 
\usepackage{amsmath} 
\usepackage[utf8]{inputenc} 
\usepackage{pgf,tikz,pgfplots} 
\pgfplotsset{compat=1.15} 
\usepackage{mathrsfs} 
%\usetikzlibrary{arrows} 
%\usetikzlibrary{decorations.markings, shapes,positioning,arrows.meta,bending,automata} 
\usetikzlibrary {arrows.meta,automata,positioning,shadows,calc}
\usecolortheme{beaver} 
\usefonttheme{professionalfonts} % using non standard fonts for beamer 
\usefonttheme{serif} % default family is serif 
\addtobeamertemplate{frametitle}{}{\vspace{-0.4em}} % decrease 
\newcommand\DoubleLine[7][4pt]{%
    \path(#2)--(#3)coordinate[at start](h1)coordinate[at end](h2);
    \draw[#4]($(h1)!#1!90:(h2)$)-- node [auto=left] {#5} ($(h2)!#1!-90:(h1)$); 
    \draw[#6]($(h1)!#1!-90:(h2)$)-- node [auto=right] {#7} ($(h2)!#1!90:(h1)$);
}
\begin{document} 
    \begin{frame}[t] 
        \begin{center}
        \begin{tikzpicture}[
            ->,
            >={Stealth[round]},
            shorten >=1pt,
            auto,
            node distance=2.8cm,
            on grid,
            semithick,
        every state/.style={
            fill=red,
            draw=none,
            circular drop shadow,
            text=white
        }
    ]
        \node[state] (A)              {$v_1$};
        \node[state] (B) [right=of A] {$v_2$};
        \node[state] (D) [below=of A] {$v_4$};
        \node[state] (C) [below=of B] {$v_3$};
        
        \path (A) edge  (B) 
        (C)edge(D)
        (D)edge(A)
        (A) edge [loop above]  (A)
        ;
        
        \DoubleLine{B}{C}{<-,very thick,black}{}{->,very thick,red}{}
        \end{tikzpicture}
    \end{center}
    \end{frame} 
\end{document}

双箭头定义取自此处——

标记图中的平行边

Answer