BuddyPress is a package built on top of WordPress which transforms it into a social network with profiles, friends, messaging, groups, and activity streams. The BuddyPress plugins can be themed to match your own style. All of the plugins can help you create a complete social network or you can use specific plugins to add special features to your blog network. Its 100% GPL and Open Source.
You can test drive the BuddyPress demo site, which is powered by the latest version of the BuddyPress software. You can sign up and see how BuddyPress works. I signed up too and the demo application is amazing.