Hello,
There's a couple of modules that may help.
The Smart-Thinker modules are primarily designed for this type of community building - I am about to release the next version of the UserGroups module and I modelled it on MySpace's Groups implementation.
You can create public or private groups, search by group category or free-text tags, join public groups, invite others to join private (or public groups) and then add Groups to Events as invites. Integrating with Scott's (Ventrians Private Messages) you can send PMs to a group (this is like a MySpace Bulletin).
The next version of the UserProfile module will lean towwards MySpaces users - youcan currently see the profile picture but I want to make some nice little controls like "Cool new users" on MySpace and do some more work with sorting. I am adding tags to everything so users can categorize data, and letting a logged off user do as much as possible (without violating privacy) without needing to log in (this encourages visitor conversions).
I think the Smart-Thinker Events module is way more advanced than MySpace's one (new version is about to be release too). All of these modules integrate with the Smart-Thinker UserProfile module so you can click on a user's name anywhere to see their profile.
For a personalized page for each user check out the Smart-Thinker HomePage module.
Check out
PokerDIY.com to see it all come together. PokerDIY is a social networking community for live poker. I will be uploading the new Groups module this weekend (tripled in size) and it will be a little clearer where it's heading...