I'm not understanding something because that looks like you're creating a table for each node type and the rows of said tables are the edges.

You've got it. The only part you're missing is that isn't "just" a graph system. It's Krang, the purpose of which is not to be a general graph implementation but rather to publish webpages. The fact that dumping and loading data is essentially a cyclic-graph-loading problem is more a side-effect than a design goal.

In this case each node type is a completely different kind of data - stories, templates, media, categories, users, etc. The links are forgeign keys in the tables, category_id in the media table for example.

Does that make sense?

-sam