Among other things it ingested xfn (and foaf) so you could reasonably look for things like the connection between you and someone else who had a webpage, but the whole thing by itself didn't replace in any way what social networks were already offering, e.g. your feed, or direct messaging.
I think WordPress still supports xfn links, but it's not particularly useful.
It didn't get to that point, but there's a lot that could be possible if the graph were owned by everyone instead of just the social network owners. Distributed trust, moderation, etc.
That's imo the real reason semweb, microformats etc.. failed. We're left with a bit of schema.org that just plays into Google's SEO tactics.
by social networks i assume you mean specifically facebook, twitter etc and not IRC or any of the other pre-existing social networks that simply didnt have profile pages or comments sections