Testing 'Six Degrees of Separation'

Are all the people on earth really connected via six steps of social connection? If you imagine that each person has at least 44 unique friends, and each friend does, and so on for six degrees...you get to more than 7 billion people, which happens to be roughly the population of our planet. It's a cool theory, but does it hold up to testing?
A variant of the "six degrees" theory (called the "small world problem") was one of many tested by Stanley Milgram (paper here [PDF]) in the 1960s. Prior to Milgram's work, mathematician Paul Erdős worked out much of the math involved. More recent tests (many of which use modern social networking sites) turn up surprising evidence about the interconnectedness of humans around the globe.
In this video, Derek from Veritasium summarizes the science behind "Six Degrees of Separation." Check it out, and watch for a special guest star right around the 7-minute mark:
Strongly related: Kevin Bacon on 'Six Degrees of Kevin Bacon.'