The Draw command accepts several options. Any arguments not of a form listed below are passed to the GraphTheory:-DrawGraph command; its help page describes these options. By default, if G is connected, the option layout = spring is passed to GraphTheory:-DrawGraph, and no options at all if G is not connected. Note that any plot options can generally be passed to GraphTheory:-DrawGraph (and therefore to the Draw command), though not all such options are useful.

vertexstylesheet = l

This option gives a list of stylesheet options to be applied to the vertices of G that correspond to the vertices of H. The default value is [color = red].

hyperedgestylesheet = l

This option gives a list of stylesheet options to be applied to the vertices v(e) of G that correspond to big hyperedges of H. The default value is [shape = hexagon, fontsize = 6, fontcolor = "_match"]. This means that the labels of these vertices will not be visible; to make the labels visible, use this option and do not include the entry fontcolor = "_match".

smalledgestylesheet = l

This option gives a list of stylesheet options to be applied to the edges of G that correspond to small hyperedges of H. The default value is [] (no special styling).

bigedgestylesheet = l

This option gives a list of stylesheet options to be applied to the edges of G that correspond to big hyperedges of H. The default value is [linestyle = dash].

output = o

By default, the Draw command returns the plot data structure corresponding to the drawing of G by the GraphTheory:-DrawGraph command. For some applications, it may be useful to use G itself, rather than the plot data structure.

If you use the option output = graph, the Draw command will return G.

If you use the option output = plot (the default), the Draw command will return the plot data structure.

If you use the option output = l, where l is a list of the names graph and plot, then the Draw command will return the corresponding values as an expression sequence. For example, if you use the option output = [plot, graph], then the Draw command will return an expression sequence P, G, where P is the plot data structure and G is the graph.

hyperedgeslabels = f

If you want to work with G, you may want to refer to its individual vertices, for example if you want to use the command GraphTheory:-StyleVertex. The vertices of G that correspond to vertices of H are the same as the vertices of H, so they can be referred to in the same way that you refer to the vertices of H. But the other vertices v(e) of G, corresponding to big hyperedges e of H, by default get a name that cannot be typed (each is a different local variable named the empty symbol).

If you specify the hyperedgeslabel option, then f is a procedure or appliable module that is applied to each big hyperedge to obtain the label of the corresponding vertex of G. Each label should be an integer, a symbol (that is, a variable name), or a string. All such labels should be distinct, and they should be distinct from the vertices of H; otherwise, an error is raised.

Note that these labels are generally not visible in the plot, because the default hyperedgestylesheet gives them a font color that matches the background color. Use the hyperedgestylesheet option if you want to see these labels in the plot.

Hypergraph : mathematically, a hypergraph is a pair (X, Y) where X  is a finite set and Y is a set of non-empty subsets of X.

Vertices : the members of X are called the vertices of the hypergraph (X, Y).

Hyperedges : the members of Y are called the hyperedges (or simply edges) of  the hypergraph (X, Y).