For 1.7 there are plugins available to turn off the public registrations. Search the community

For 1.8 : its available with the core, itself.

But if you can that of accepting users by invitation only?

Admins can always create accounts even if public registration is turned off.

Can we be equal to (Tuenti ;)?

Tuenti does their invites differently -
more logic than Elgg does with 'Private' site.
The invitation is sent by existing member -
and then Tuenti will give regard to new user registering..

That's what I want to do with my network