[Tex/LaTex] How to draw a poset Hasse Diagram using TikZ

diagramstikz-pgf

I need to draw an Hasse Diagram using LaTeX. TikZ is the solution I would like to use. I tried with a simple structure involving trees but obviously when I need to join two nodes, it is not possible.

I searched a little but found no immediate solutions for Hasse Diagrams in TikZ. Which one is the fastest structure I can use? I would like also to have the tree syntax flexibility without manually specifying where nodes should be places. I just want to specify nodes and connections.

Best Answer

Here is a brief tutorial to get you started: As in any other piece of software, break it down into its components.

  1. First step is to draw the nodes and give them name. Lets start with the top node located at the origin and name it (top):

    \documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    \node (top) at (0,0) {$\{x,y\}$};
\end{tikzpicture}
\end{document}

    So now you have:

    enter image description here

    which is not too exciting.

    Note: I included the full code here, but subsequent steps I show only the additions to the above to make it easier to follow.

  2. Next, add the left and right nodes. These should be located relative to the (top) node so that in case we decide to move the position of the top node, these two will move along with it:

    \node [below left  of=top] (left)  {$x$};
\node [below right of=top] (right) {$y$};

    So, now things a looking a bit more useful:

    enter image description here

    If these are not far enough apart, you could move them, again relatively, by using something like xshift=<length>, or xshift=<length>.

  3. Next step is to draw the lines connecting these nodes via their node names (color used here to see the correspondence between the code and the output):

    \draw [red,  thick] (top) -- (left);
\draw [blue, thick] (top) -- (right);

    to get:

    enter image description here

    If the lines are not long enough you can shorten then via a negative amount. For the top we use shorten <=-2pt, and for the bottom shorten >=-2pt to get:

    enter image description here

    Using the to syntax as opposed to the -- allows you to get fancier and control the angle at the out point via out=<angle>, and the angle of the line coming in via in=<angle>:

    \draw [red,  thick, shorten <=-2pt, shorten >=-2pt, out=-120, in=90] (top) to (left);
\draw [blue, thick, shorten <=-2pt, shorten >=-2pt, out=-60,  in=90] (top) to (right);

    which if it had been used below would have produced:

    enter image description here

    As pointed out by Paul Gaborit, the out and in options are really only for the to directive so some might prefer a syntax that more explicitly places those options for the to as in:

    \draw [red,  thick, shorten <=-2pt, shorten >=-2pt] (top) to [out=-120, in=90] (left);
\draw [blue, thick, shorten <=-2pt, shorten >=-2pt] (top) to [out=-60,  in=90] (right);

References:

Other tutorial like answers here which might be useful for new tikz users include:

Code:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    % First, locate each of the nodes and name them
    \node (top) at (0,0) {$\{x,y\}$};
    \node [below left  of=top] (left)  {$x$};
    \node [below right of=top] (right) {$y$};

    % Now draw the lines:
    \draw [red,  thick, shorten <=-2pt, shorten >=-2pt] (top) -- (left);
    \draw [blue, thick, shorten <=-2pt, shorten >=-2pt] (top) -- (right);
\end{tikzpicture}
\end{document}
Related Question