Is is possible to create a private tree?

I'm just beginner and planning to create an own tree in Geni. Is it possible to create a private tree so, that even when searching in internet there would be no Geni results at all?

Now my own account is private, but relatives I added in my tree can be found with an internet search - and relationships as well. When I search my brother in Google like "firstname lastname" and choose the appearing Geni-page from results, all other names and relationships can be seen - but in my box there is only a text "Private User".

I rather would not see any names and relationships at all. I wish only the people I call into my tree could see the tree in geni and names/relationships in internet search. Or do I something wrong?