4.74 Degrees of Separation
This story in the New York Times summarizes a recently published study about interconnectedness on Facebook.
A computational analysis of the 721 million worldwide Facebook users shows that the average distance between two people is about 4.74 “friends”. Roughly speaking, given anyone in the world on Facebook, a friend of your friend is likely to be friends with a friend of their friend.
An amazing result! And a cool application of graph and network theory. Now the questions becomes “What can we do with this knowledge?”
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Mr Honner 
“What can we do with this knowledge?”
Well, there are already (technically) some applications, not only with social media, but even when it comes to programming or statistics.
Statistically-wise, take Klout, for instance. As for programming, something as overlooked as a spell-checker uses this concept; in this case, it would be the “edit distance” for determining the best choices for correcting a word or phrase. It helps narrow down the possible words or phrases the user could have meant by finding perhaps the top x words/phrases, x being a positive integer (top 3, top 5, etc.). The shortest edit distance is the best match. It goes down from there, ‘going down’ referring to the pop-up list that you see when right-clicking the misspelled word (visually referring to Microsoft Word).
Interesting point about “edit distance”. I had never thought about viewing a dictionary (of both correctly and incorrectly spelled words) as a graph. Is that really how a spell-checker works? Fascinating.