Joseph and Pharaoh Are Now Friends -- Small Worlds and Networks

April 1, 2009
Posted by Jay Livingston

I checked my Facebook page – something I do regularly once a month or so – and discovered that Anomie* had posted a link to The Facebook Haggadah by Carl Elkin. The Passover story written as a series of Facebook messages (“Pharaoh has taken the Which god are you? quiz” “25 things you didn't know about me by God. 1. Guilty pleasure: Smiting people. . . .”) And so on.

I sent the link to a few people, including my niece. She e-mailed me back:

Not only is that hilariously funny, I KNOW the guy who did it! Carl Elkin lived in my room in my old apartment before I did. Now he's married to a girl I knew from Amherst. Small world. . .

My first thought was that it wasn’t really so surprising. How many degrees of separation should I expect between me and the author of the Haggadah? He’s considerably younger, but we live in the same geographic area (Northeast urban corridor) and in the same social-cultural world. If there isn’t someone we know in common, then I probably know someone who knows someone who knows him. Two degrees of separation.

That’s the way it usually works. It’s not that the world is small but that it’s organized in a way that makes for shorter paths connecting people.
The connections run through a few people who are connected to a lot of people. I may not be connected to very many people, but at least one of my connections will be one of these “nodal” people (the brightly colored dots on the central line running through the diagram**). Think of it in Facebook terms: I have only 18 Facebook friends. But I can be easily connected to someone else because at least one of my friends is one of those nodal people with 850 friends (what my son calls “a Facebook whore.”)

But my niece was right. This connection was a surprise because it didn’t followthe usual network pattern of going up to a well-connected person. Instead, it was more like what we mean when we use the phrase “small world.” The world of East Coast academia and related areas just isn’t all that big, with a relatively small number of student apartments to move in and out of and a relatively small number of possible marriage partners (especially if you limit your choices by religion and that religion is Judaism – even in the Northeast Academic Corridor).

*Anomie credits Eszter, who posted the link at Crooked Timber.

** The diagram is from Wikipedia.