Drawing a bijective map with TiKz

Question

I am trying to produce a diagram similar to the following (from Wikipedia)

Bijection

in TiKz. Now, I thought this would be relatively simple, however, I am having trouble getting the elements (the dots) to be of the correct size and am unsure how to elegantly surround the elements in an ellipse. My current TiKz code is

\documentclass{article}
\pagestyle{empty}
\usepackage{tikz}
\usetikzlibrary{calc,trees,positioning,arrows,chains,shapes.geometric,%
    shapes,shadows,matrix}

\begin{document}
\begin{figure}
 \centering
 \begin{tikzpicture}[ele/.style={fill=black,minimum size=2pt,circle}, node distance=7pt]
  \node[ele] (a1) {};
  \node[ele] (a2) [below=of a1] {};
  \node[ele] (a3) [below=of a2] {};
  \node[ele] (a4) [below=of a3] {};
  \node[ele] (b1) [right=of a1,xshift=15pt] {};
  \node[ele] (b2) [below=of b1] {};
  \node[ele] (b3) [below=of b2] {};
  \node[ele] (b4) [below=of b3] {};
  \draw[->,thick] (a1) -- (b4);
  \draw[->,thick] (a2) -- (b2);
  \draw[->,thick] (a3) -- (b1);
  \draw[->,thick] (a4) -- (b3);
 \end{tikzpicture}
\end{figure}
\end{document}

which renders as

Mine

Can anyone recommend a more elegant means of drawing such a diagram?

Set inner sep in the ele style to 0. – Caramdir Jun 05 '11 at 20:22 — Caramdir, Jun 05 '11 at 20:22

Alain Matthes · Accepted Answer · 2011-06-05T21:37:40.680

\documentclass{article}
\pagestyle{empty}
\usepackage{tikz}
\usetikzlibrary{calc,trees,positioning,arrows,fit,shapes,calc}

\begin{document}
\begin{figure}
 \centering
 \begin{tikzpicture}[ele/.style={fill=black,circle,minimum width=.8pt,inner sep=1pt},every fit/.style={ellipse,draw,inner sep=-2pt}]
  \node[ele,label=left:$a$] (a1) at (0,4) {};    
  \node[ele,label=left:$b$] (a2) at (0,3) {};    
  \node[ele,label=left:$c$] (a3) at (0,2) {};
  \node[ele,label=left:$d$] (a4) at (0,1) {};

  \node[ele,,label=right:$1$] (b1) at (4,4) {};
  \node[ele,,label=right:$2$] (b2) at (4,3) {};
  \node[ele,,label=right:$3$] (b3) at (4,2) {};
  \node[ele,,label=right:$4$] (b4) at (4,1) {};

  \node[draw,fit= (a1) (a2) (a3) (a4),minimum width=2cm] {} ;
  \node[draw,fit= (b1) (b2) (b3) (b4),minimum width=2cm] {} ;  
  \draw[->,thick,shorten <=2pt,shorten >=2pt] (a1) -- (b4);
  \draw[->,thick,shorten <=2pt,shorten >=2] (a2) -- (b2);
  \draw[->,thick,shorten <=2pt,shorten >=2] (a3) -- (b1);
  \draw[->,thick,shorten <=2pt,shorten >=2] (a4) -- (b3);
 \end{tikzpicture}
\end{figure}
\end{document}

enter image description here

Why did you hard code the coordinates, for example, (4,4), etc? The OP did not use such hardcoded coordinates. And I think using hardcoded coordinates makes future update much harder. What do you think?
I found another related answer but without hardcoded coordinates here. — Display Name, Mar 31 '21 at 11:33

score 1 · Answer 2 · answered Jun 03 '18 at 17:56

Wallner's answer was one of the best mapping diagram I have ever seen. I modified his code for your problem

\begin{figure}[ht]
\centering
\begin{tikzpicture}
    % draw the sets
    \filldraw[fill=blue!20, draw=blue!60] (-1.5,0) circle (1cm);
    \filldraw[fill=red!20, draw=red!60] (1.5,0) circle (1cm);


    % the texts
    \node at (-1.5,1.5) {$X$};
    \node at (1.5,1.5) {$Y$};

    % the points in the sets (here I just create nodes to use them later on to position
    % the circles and the arrows
    \node (x1) at (-1.5,0.7) {$a$};
    \node (x2) at (-1.5,0.3) {$b$};
    \node (x3) at (-1.5,-0.2) {$c$};
    \node (x4) at (-1.5,-0.7) {$d$};
    \node (y1) at (1.5,0.7) {$1$};
    \node (y2) at (1.5,0.3) {$2$};
    \node (y3) at (1.5,-0.2) {$3$};
    \node (y4) at (1.5,-0.7) {$4$};

    % draw the arrows
    \draw[->] (x1) -- (y4);
    \draw[->] (x2) -- (y2);
    \draw[->] (x3) -- (y1);
    \draw[->] (x4) -- (y3);

\end{tikzpicture}
\caption{Mapping diagram of relation $S$}
\end{figure}

which produce the mapping below:

Drawing a bijective map with TiKz

2 Answers2

Linked

Related