Buddypress Invitation Only

WP Admin > Settings > BuddyPress > Options. Enable membership invitations by ticking the checkbox labeled “Allow registered members to invite people to join this network.”

Then turn off registrations in the Settings > General tab. (checkbox, anyone can register)

On the “Manage Invitations” screen, (Tools > Buddypress) site admins can view pending and accepted invitations and choose to resend the email or cancel the invitation.