I am connected (on LinkedIn) to at least one person who is directly connected to Barack Obama. That's one degree of separation. With Bill Gates, I have two degrees of separation.
Social networks have made it possible for people to be more closely related than ever before. Actually, I'm much closer to Bill Gates than Barack Obama, in real life. I'd expect (in real life, as opposed to online) that my degrees of separation with the US President would be 4 or 5, and 3 with Bill.
only has 5 direct connections on LinkedIn. Both myself
and Barack Obama
have 500+, according to LinkedIn. Actually, both of us have far more than 500 direct connections. This explains why I'm apparently so close to the President.
For those interested in the mathematics, here's a little brain teaser: what are the chances that your degrees of separation with someone on LinkedIn is one, if both you and the person in question have 3000 connections? My guess, just a very rough guess: it is more than 10%.