It's probably worth pointing out that a graph consists of nodes and edges. The Internet (protocol(s)) standardized building & discovering nodes, but they are not standardizing edge discovery. And they only cover a very ephemeral mode of edge building.

That is what the social graph is about - making it possible to describe and discover the edges.

What would you hope to have / expect to find for edge discovery? Any examples?

What types of edges might you want to have that existing models don't support?

The things a social graph gives you - Friends of a Friend, graph overlap, graph complexity, etc.

All these metrics matter a lot in the social space. We can't get them (with, see below, a few exceptions like HTML - and boy is having the edges there a useful thing)

So, relationships, essentially.

An article I ran acrosss a few days back pointed out how the nature relationships also matters. It starts off noting that gender is often given as binary (M/F), when reality can be more complicated (though most of the complications are a distinct minority case). That's something I ran across years back looking at healthcare data, where "gender" had in some cases five values: male, female, indeterminate, other, and unknown.

Relationships, though: "friend", "family", "co-worker", "ex-spouse", "enemy", ...

Any thoughts on capturing something such as this (or of similar complexity) on a graph? Or references?

I suspect international or inter-corporate relationships might be similar.

There have been attempts:

FOAF: https://en.wikipedia.org/wiki/FOAF_(ontology)

XFN: https://en.wikipedia.org/wiki/XHTML_Friends_Network

There's probably more. There's always more standards :)

So many to choose from!

ummm, href?

That's HTML. One of the many things layered on top of "The Internet protocols". It's not exactly a core protocol :)