One of my Graph Drawing papers, Upright-Quad Drawing of st-Planar Learning Spaces, is now up at the arXiv. It's about graphs formed from antimatroids by drawing edges between pairs of sets that differ in a single element, but it's also about a principle that I think can apply more generally in graph drawing: if you're drawing graphs with a special structure, then the drawing should make the structure visually apparent: it should be of a type that exists only for graphs having that structure.

E.g., if you have an application where it's important that its graphs are planar, then they should be drawn without crossings so that people looking at them can see that they're planar. For the graphs I'm interested in here, the structure is made apparent by a drawing in which all faces are quadrilaterals with the bottom and left sides parallel to the coordinate axis (and where the drawing has unique top-right and bottom-left vertices); such a drawing only exists for graphs coming from antimatroids. The paper also outlines close connections between these graph drawings and arrangements of pseudolines formed by translates of a 90-degree wedge; as shown below, if you draw the dual of such an arrangement by placing a vertex at the top right corner of each region, you get a drawing of this type. (The dotted lines in the right side of the drawing are the parts of the pseudolines not covered by graph edges.)

An arrangement of orthogonal pseudolines, and its dual graph drawn with upright-quadrilateral faces

Coincidentally, today I also ran across this diagram of GCSE math topics on bodmas; it shows in a less formal way the same sort of thing I'm trying to approach with this paper: diagrams of concepts from some body of knowledge and the prerequisites necessary to learn them.