The key to NOT being such a short hop away from everyone on the planet is to not let them into your life in the first place. Yes, some people -- perhaps even most of them -- will just blindly accept friend requests unconditionally, giving them thousands of "friends" who are just names on a list.
The only reason I touch Facebook at all, and then only with all of what flimsy privacy protection they offer enabled, is to easily keep contact with actual friends from that bizarre world called Real Life. With a handful of exceptions (because I telecommute and don't visit the home office often enough to meet all my colleagues face-to-face) all my friends on Facebook are people I have met in person and had more than a fleeting acquaintance with. I happily befriended Praneeth and Sasideep even though I have never met them in person being as how they are on the other side of the planet, but I work with them every day. On the other hand I'll probably never add Bob from accounting because my only contact with him in 25 years has been a question about a travel expense.
I don't accept requests from friends or relatives of my friends either, until I have met them in person. I'm sure my friend Paul's brother Ron is a great guy, but we have nothing to do with each other, no reason to speak to each other, no interest in each other's careers or families or hip surgery or lottery winnings.
Some of my friends feel the same way; others (mostly the younger ones, children of my peer group) go with the "friends with the world" approach. So I like to think I'm keeping my degrees of separation to an acceptably high number, and I intend to keep it that way as long as it is within my power.