The page i posted does offer many options, be wary of the animated one, i purchased that software years ago and it was the worst support i have ever experienced
The reason i have not bothered is that i think you must commit big time and at the moment that does not suit, plus is would have to really suit my needs, i was maybe going to try get Friend.Singles up and running
Working for a webhost I think I encounter someone aiming for a big social networking success at least once a week. To be honest haven't heard/seen none of them gaining much popularity (apart from maybe some small local community) but judging by opinions and feedbacks I believe Dolphin by Boonex and Oxwall would be pretty great choices to start.
That being said consider that such applications (well some of their functionalities mostly) are quite the resource hogs and will quickly outgrow a shared hosting platform.