[Tex/LaTex] How to draw edges with a bend

Question

I want to draw a diagram given below. Till now I am able to this much.

\documentclass{beamer}
\usepackage[most]{tcolorbox}
\usepackage{multirow}
\usetikzlibrary{matrix, arrows.meta, calc, positioning}
\tikzset{myarrow/.style={-Latex, rounded corners},}

\newtcolorbox{mybox}[1][]{%
 colback=bg, 
 colframe=blue!75!black,
 fonttitle=\bfseries,
 coltitle=blue!75!black,
 colbacktitle=bg,
 enhanced,
 attach boxed title to top left={yshift=-1.2mm, xshift=2mm},
 title=#2,
 #1}

\begin{document}

\begin{tikzpicture}    
\node (a) at (0,0) {$a_i$};    
\node (b) at (3,0) {$a_{ij}$};    
\node (c) at (7,0) {$a_{j}$};    
\node  (d) at (3,3) {$a_k$};    
\draw[-latex,bend right]  (a) edge (b);    
\draw[-latex,bend left]  (a) edge (b);
\draw[-latex,left]  (c) edge (b);    
\draw[-latex,left]  (b) edge (d);    
\end{tikzpicture}

\end{document}

I am using code in this frame :

\begin{frame}{GroupIso many-one reduces to DirGI }

\begin{mybox}{GroupIso $\le_m$ DirGI }
\begin{itemize}        
    \item Group table can be seen as a set of equations of the form $a_i \circ a_j =a_k$        
    \item Each such equation will be   translated into several edge connections as follow:       
    \item  \begin{tikzpicture}    
    \matrix[    
        matrix of math nodes,    
        row sep=30pt,    
        column sep=30pt,     
        nodes={circle, draw, text height=1.75ex, text depth=.5ex, 
            text width=width("$a_{ij}$"), text centered}    
        ] (m) {    
        & a_i \\    
        a_{ij} & a_{j} & a_k\\
    };
    \draw[myarrow] (m-2-3) -- (m-2-2);     
    \draw[myarrow] (m-2-2) -- (m-1-2);    
    \draw[myarrow] (m-2-2.135) -- +(-4pt, 4pt) -- ([shift={(4pt, 4pt)}]m-2-1.45) -- (m-2-1.45);    
    \draw[myarrow] (m-2-1.-45) -- +(4pt, -4pt) -- ([shift={(-4pt, -4pt)}]m-2-2.-135) -- (m-2-2.-135);    
    \end{tikzpicture}       
\end{itemize}  
\end{mybox}

\end{frame} 

and output I am getting is

see the compiled output

I want to draw:

I want the nodes to look like small circles and, second problem, how to draw multi-edges with a bend?

Answer 1

With a matrix and the anchoring with the degrees, the code could be simplyfied:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix, arrows.meta, calc, positioning}
\tikzset{myarrow/.style={-Latex, rounded corners},}
\begin{document}

    \begin{tikzpicture}
    \matrix[
        matrix of math nodes,
        row sep=30pt,
        column sep=30pt, 
        nodes={circle, draw, text height=1.75ex, text depth=.5ex, 
            text width=width("$a_{ij}$"), text centered}
        ] (m) {
        & a_i \\
        a_{ij} & a_{j} & a_k\\
    };
    \draw[myarrow] (m-2-3) -- (m-2-2); 
    \draw[myarrow] (m-2-2) -- (m-1-2);
    \draw[myarrow] (m-2-2.135) -- +(-4pt, 4pt) -- ([shift={(4pt, 4pt)}]m-2-1.45) -- (m-2-1.45);
    \draw[myarrow] (m-2-1.-45) -- +(4pt, -4pt) -- ([shift={(-4pt, -4pt)}]m-2-2.-135) -- (m-2-2.-135);
    \end{tikzpicture}

\end{document}

Edit (reply to the OP's edit):

Well, I cannot reproduce your problem because I get some errors if I use your MWE with beamer.

However, putting a tikzpicture inside an itemize, which is inside a tcolorbox, which is in a beamer frame seems quite challenging (but it is possible without using \matrix, like in AboAmmar's answer, or adding ampersand replacement=\& to the matrix options, like in marmot's one).

I suggest to you to create a .pdf of your image with this code, let's call it myimage:

\documentclass[tikz]{standalone}
\usetikzlibrary{matrix, arrows.meta, calc, positioning}
\tikzset{myarrow/.style={-Latex, rounded corners},}
\begin{document}

    \begin{tikzpicture}
    \matrix[
    matrix of math nodes,
    row sep=30pt,
    column sep=30pt, 
    nodes={circle, draw, text height=1.75ex, text depth=.5ex, 
        text width=width("$a_{ij}$"), text centered}
    ] (m) {
        & a_i \\
        a_{ij} & a_{j} & a_k\\
    };
    \draw[myarrow] (m-2-3) -- (m-2-2); 
    \draw[myarrow] (m-2-2) -- (m-1-2);
    \draw[myarrow] (m-2-2.135) -- +(-4pt, 4pt) -- ([shift={(4pt, 4pt)}]m-2-1.45) -- (m-2-1.45);
    \draw[myarrow] (m-2-1.-45) -- +(4pt, -4pt) -- ([shift={(-4pt, -4pt)}]m-2-2.-135) -- (m-2-2.-135);
    \end{tikzpicture}

\end{document}

And then include myimage in your presentation (see the commented code if you want the \item before the image):

\documentclass{beamer}
\usepackage[most]{tcolorbox}
\usepackage{multirow}
%\usepackage[export]{adjustbox} if you want the \item before the image

\newtcolorbox{mybox}[2][]{% I put [2] because with [1] I could not compile
    colback=bg, 
    colframe=blue!75!black,
    fonttitle=\bfseries,
    coltitle=blue!75!black, 
    colbacktitle=bg,
    enhanced,
    attach boxed title to top left={yshift=-1.2mm, xshift=2mm},
    title=#2,
    #1}

\begin{document}
\begin{frame}[fragile]{GroupIso many-one reduces to DirGI }
\begin{mybox}{GroupIso $\le_m$ DirGI}
    \begin{itemize}
        \item Group table can be seen as a set of equations of the form $a_i \circ a_j =a_k$
        \item Each such equation will be   translated into several edge connections as follow:\newline
        %\item \includegraphics[width=.5\linewidth,valign=t]{myimage} %if you want the \item before the image
        \includegraphics[width=.5\linewidth]{myimage}
    \end{itemize}
\end{mybox}
\end{frame}
\end{document}

The result is: