Simple directed hypergraphs in TikZ

Question

I'm looking for a simple way in Tikz to draw directed hypergraphs, where the hyperedges are ordered pairs of sets of vertices. For example I would like the hyperedges ({a,b},{c}) and ({c},{a,b}) to be presented like this:

The "in" vertices (on the left) should be vertically aligned, as should the "out" vertices (on the right). For my purposes, there are never more than two "in" vertices or two "out" vertices, and I would be happy to have this baked into the solution. The solution should be flexible enough to accommodate node labels larger than the single characters shown here.

I would also like to be able to assemble these into larger hypergraphs, as shown here, in which case the arms of the hyperedges need not be of the same length:

although the "direction" will always be read from left to right. I'm not concerned with overlapping lines (I'll only be working with simple graphs and will be able to arrange things so lines don't overlap).

It should be easy to move the nodes around for aesthetic reasons, so that for example the following is the graph above but laid out slightly differently:

The title of this question is similar, but my requirements are slightly different.

Answer 1

A second attempt, this time making some assumptions on the layout. I assume you want the hyper-edge to always be aligned to the "lonely" node of the triplets (e.g. c in ({a,b},{c}) and ({c},{a,b}) ).

Since you seem to need fine control on the positioning of the nodes I suggest the following: first you place named nodes with manual positioning (using whichever method you prefer, from absolute coordinates to relative positioning); then you specify the hyperedges and the corresponding arcs get created. Here's a macro that can help you with the second step:

\newcommand{\hyperedge}[4][180]{
     \draw (#2.#1) ++(#1:.5)  edge (#2) edge (#3) edge (#4);
}

It takes 4 arguments (first optional): \hyperedge[angle]{c}{a}{b} draws the edges assuming that c is the lonely node and requires you to specify the angle at which the hyperedge should stick out of it.

The definition of the macro works by moving to the right/left border of the lonely node (this is accomplished by (#2.#1) which moves to the border of the node #2 at angle #1), then move right/left by .5 which is the coordinate of the "centre" of the edge; then this "centre" is connected with the nodes using the edge action.

Here's your second example using tikz and my macro:

\documentclass{standalone}
\usepackage{tikz}

\newcommand{\hyperedge}[4][180]{
     \draw (#2.#1) ++(#1:.5)  edge (#2) edge (#3) edge (#4);    
}

\begin{document}
\begin{tikzpicture}[
    y=.7cm, x=1cm,
    every edge/.append style={thick}
]

\node (a) at (-1,1) {a};
\node (b) at (-1,-1) {b};
\node (c) at (0,0) {c};
\node (d) at (1,1) {d};
\node (e) at (1,-1) {e};
\node (g) at (2,-2) {g};

\hyperedge{c}{b}{a}
\hyperedge[0]{c}{d}{e}
\hyperedge{g}{b}{e}


\end{tikzpicture}

\end{document}

Which is rather readable and easy to extend.

You can elaborate on this by using other means to specify the angle (other derived macros) or enriching it with custom styles.

Another option for the placement of the "centre" of the hyperedge is barycentric coordinates:

\newcommand{\hyperedge}[3]{
    \draw (barycentric cs:#1=1,#2=1,#3=1) edge (#1) edge (#2) edge (#3);
}

Note that this does not require the angle argument.

Answer 2

This simple example should get you started

\documentclass{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[
    every edge/.append style={thick}
]

\coordinate (e1) at (0,0);

\path (e1) (130:1) node[circle] (a) {a};
\path (e1) (230:1) node[circle] (b) {b};
\path (e1) (0:.8) node[circle] (c) {c};

\draw (e1) edge (a) edge (b) edge (c);

\end{tikzpicture}

\end{document}

Here I choose to position the hyper-edge (e1) first and position the nodes relative to it by using \path then moving to the coordinate of the edge (e1) than moving somewhere from there and placing a node. The coordinates (angle:radius) are polar, the ones (x,y) are cartesian.

The actual "branches" of the hyper-edge are drawn by the \draw command using the edge action which uses the first node as the starting point and connects all the others to it.

Adding other parts of the graph should be easy using these building blocks. Since you seem to want rather precise control on the positioning of the nodes/edges I am not attempting at anything more general/automatic.