We already have an open graph, its the Internet Protocol and associated addresses. All other experiences that are delivered over IP are just sub-protocols with attached UX that is preferable for the users.
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.
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)
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.
That is what the social graph is about - making it possible to describe and discover the edges.