The focus of this class was a discussion of Stanley Milgram’s Experiment from 1967 that is widely credited for suggesting that the “social distance” between individuals is quite small. In other words, the “degree of separation” between individuals is small. There are many problems with the experiment, but the experiment has been repeated a number of times with different parameters and in other settings and has produced similar results. For a recent example, look at this news item claiming that the the degree of separation in Facebook is 4.74! In fact, if you want to participate in a current “small-world experiment”, you might want to enroll in Yahoo!’s small-world experiment.
These ideas depend on the notion of “distance” in a graph. Here are slides in which I define distance, diameter, and average path length in graphs. We spent a few minutes in class calculating these measures for a small, example graph. My hope is that this will help you better understand some of your readings on “small world” networks.
Homework for next class (9/19): Read “The Third Link” on “Six Degrees of Separation” from the textbook. Be prepared to discuss your reading.