# How can I draw the following directed graph?

How can I make such a graph using tikz?

I can draw the circled nodes and the arrows, but I can't change their position. (e.g. the one that starts from node 1 and ends at node 3).

Edit: I would prefer straight arrows and not curved ones, just as in the drawing.

A more straight forward approach may be using the graph library, (requires LuaLaTeX, though). Here is the code using graph library:

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{graphs,graphdrawing,arrows.meta}
\usegdlibrary{circular}
\begin{document}
\tikz[>=Stealth]\graph[simple necklace layout, nodes={circle,minimum size=.7cm,draw}, node sep=1cm]{
1,2,6,4,5,3;
1->[xshift=1pt,yshift=2pt]3 -> 2, 3 ->[xshift=-1pt,yshift=-2pt]1 -> 2;
3 -> 5 -> 6 ->[xshift=-1pt,yshift=-2pt] 4 ->[xshift=1pt,yshift=-2pt]5, 5 ->[xshift=-1pt,yshift=2pt] 4 ->[xshift=1pt,yshift=2pt] 6;
};
\end{document}

This outputs:

Another possibility could be using a matrix of nodes as follows:

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{matrix,arrows.meta}
\begin{document}
\begin{tikzpicture}[>=Stealth,->,line width=.7pt]
\matrix [matrix of math nodes,
column sep={1.5cm,between origins},
row sep={2.2cm,between origins},
nodes={circle, draw, minimum size=1cm}]
{
& |(1)| 1 &   & |(2)| 2 & \\
&  & |(3)| 3 &  \\
& |(6)| 6 &   & |(5)| 5 & \\
&  & |(4)| 4 &   \\};
\draw (1)--(2);
\draw (3)--(2);
\draw[transform canvas={xshift=2pt,yshift=2pt},shorten <= -1pt] (3)--(1);
\draw[transform canvas={xshift=-2pt,yshift=-2pt},shorten <= -1pt] (1)--(3);
\draw (3) -- (5);
\draw (5) -- (6);
\draw[transform canvas={xshift=2pt,yshift=-2pt},shorten >= -1pt] (4) -- (5);
\draw[transform canvas={xshift=-2pt,yshift=2pt},shorten >= -1pt] (5) -- (4);
\draw[transform canvas={xshift=2pt,yshift=2pt},shorten <= -1pt] (4) -- (6);
\draw[transform canvas={xshift=-2pt,yshift=-2pt},shorten <= -1pt] (6) -- (4);
\end{tikzpicture}
\end{document}

which now gives:

You may use the positioning library of tikz as stated in the comments of your question. I used the shorten code in drawing arrows to connect them to the circle. Because, when you shift them, a white ugly space appears between the arrow and circle.

%pdflatex
\documentclass[margin=0.5mm]{standalone}

\usepackage{tikz}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}
\pgfmathsetmacro{\shift}{0.25ex}

\node [draw , circle] (1) at (-0.5,3) {1};
\node [draw , circle] (2) at (0.5,3) {2};
\node [draw , circle] (3) at (0,2) {3};
\node [draw , circle] (4) at (0,0) {$4$};
\node [draw , circle] (5) at (0.5,1) {$5$};
\node [draw , circle] (6) at (-0.5,1) {$6$};

\draw [->] (1) -- (2);
\draw [->,shorten <=-1pt, transform canvas={xshift=-\shift,yshift=-\shift}] (1) -- (3);
\draw [->,shorten <=-1pt, transform canvas={xshift=\shift,yshift=\shift}] (3) -- (1);
\draw [->] (3) -- (2);

\draw [->] (3) -- (5);

\draw [->] (5) -- (6);
\draw [->,shorten <=-1pt, transform canvas={xshift=-\shift,yshift=\shift}] (4) -- (5);
\draw [->,shorten <=-1pt, transform canvas={xshift=\shift,yshift=-\shift}] (5) -- (4);
\draw [->,shorten <=-1pt, transform canvas={xshift=-\shift,yshift=-\shift}] (6) -- (4);
\draw [->,shorten <=-1pt, transform canvas={xshift=\shift,yshift=\shift}] (4) -- (6);

\end{tikzpicture}
\end{document}

With the help of the first comment, I made what I wanted (Ι made sth similar to the original drawing)! Here's the code.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{arrows.meta,shapes.misc,patterns,shapes.symbols,decorations.pathreplacing,decorations}

\begin{document}

%===Credits to JLDiaz for the following part=========

\pgfdeclaredecoration{sl}{initial}{
\state{initial}[width=\pgfdecoratedpathlength-1sp]{
\pgfmoveto{\pgfpointorigin}
}
\state{final}{
\pgflineto{\pgfpointorigin}
}
}

\tikzset{parallel arrow/.style={->,
shorten >=2mm, shorten <=2mm,
decoration={sl,raise=1mm},decorate}}
%===================================================================

\tikzset{shorten arrow/.style = {->, shorten >=2 mm, shorten <=2mm}}

\begin{tikzpicture}
\draw (0,3) circle (8pt)node[](1){1} ;

\draw (3,6) circle (8pt)node[](4){4} ;
\draw (6,3) circle (8pt)node[](3){3} ;
\draw (0,0) circle (8pt)node[](2){2} ;
\draw (3,3) circle (8pt)node[](5){5} ;
\draw (3,0) circle (8pt)node[](6){6} ;

\foreach \x in {1,3,5}
\path (4) edge[shorten arrow] (\x);

\foreach \x/\y in {1/2,2/1,2/6,6/2,5/6,6/5}
\path (\x) edge [parallel arrow] (\y);

\path (2)edge[shorten arrow] (5);

\path (5)edge[shorten arrow] (3);

\end{tikzpicture}

\end{document}

A solution with :

% arara: pdflatex

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}
$\begin{tikzcd}[% row sep = 20mm, column sep = 20mm, % both optional, adapt as you please cells={nodes={circle, draw}}, every arrow/.append style={shorten <= 1mm, shorten >= 1mm}] % both optional. Default connects the arrow directly to the circles & 4 \arrow{dl} \arrow{d} \arrow{dr} & \\ 1 \arrow[shift left]{d} & 5 \arrow[shift left]{d} \arrow{r} & 3 \\ 2 \arrow[shift left]{u} \arrow{ur} \arrow[shift left]{r} & 6 \arrow[shift left]{l} \arrow[shift left]{u} & \end{tikzcd}$
\end{document}

If the default distance for shift left is not good for you, you can just add =any_measure to it. In this case, I would define a style shifted in order to change the value in just one place.