actually is there a schema of the graph?
you said "directed", hence there should some hierarchy in it too.'
I'm not sure I understand what you're asking, but the hierarchy is based on
the relation between a category and its subcategories.
In more technical terms, in the directed graph of categories, edges are
from a category to its subcategories.
I read there are 50K+ categories, maybe is there any
list of "directions"
aka "links" of how categories are connected?
Actually, there seem to be 1M+ categories (though not all of them are
normal article categories). And category-subcategory links is exactly what
the categorylinks dump contains, along with category-page links.