Oh yes, edges of different types and their direction are definitely what the author of the post was missing.

This is precisely where triple (hyper) graphs and the idea of semantic networks comes in. Unfortunately, the designs, architecture and implementation of the semantic web are all completely impractical garbage.

I did a lot of research on rendering ontologies and in general the best way to do so is not at all. Instead try to do domain specific bijective projections (akin to DSLs). And if you really need graphs do not render the edges. It always leads to chaos, it is better to show all vertices and only display edges on request (e.g. on hover).