In class we discussed the small-world phenomenon (six degrees of separation) and how this result is not entirely surprising if exponential growth between steps are taken into account. The site http://aimfight.com/ gives you a score equal to the “sum of the current number of people online who have you listed as a buddy, out to three degrees.” Using this as a rough proxy for the real world, we can see two important points drawn in lecture, first that the effects of triadic closure drastically limits the number of connections gained from each additional degree of separation, and secondly that even with this limitation we can still connect a very large number of people with a couple of steps.
Right now there are 33 people online on my buddy list. If we use the most naive model then my score (number of “buddies” online, out to three degrees) should be roughly 33×33x33 or 36,000. However, my actual score falls far short of that, a measly 15,500. If I then reverse-calculate the number of unique “buddies” each of my “buddies” likely had, I come to an average value of 21 “buddies” each. This number is only about 66% of what I naively predicted, but explainable. My buddy list consists of three major groups: friends from Cornell, friends from high school, and others (family, work associates, etc.). If I assume an equal number of people in each group (which as of this moment is pretty accurate) and that everyone in each group is likely to be linked to everyone else in their group, then the value of 66% is actually almost mathematically intuitive. Each of my connections are only bringing in unique links from the other two groups, i.e. unique links from a “buddy” in my family group comes mainly from their college and high school groups (or whatever fitting analogous groups) and not from their family group. So, we see that triadic closure did have a major effect, even in this rough model.
The other point that can be drawn from this simple model is the reach of six degrees of separation. If we continue our calculation (of a factor of 21 growth at each step) then at 6 degrees, I should have a score of 140 million. Which is about 2.25% of the world population. Considering that it is 4am and only about a quarter of my “buddies” are online, the fact that only about 17% of the world population has internet, and that not everyone with internet (or even everyone I know) chooses to use the AOL instant messenger program, then I think that, it would not be too far of a stretch to say that at full potential, I could connect to the majority of internet users in six steps or less.
Your score does not depend on who is on your personal buddy list. It depends only on those who include you on theirs. While it’s likely that most people on your list have you on theirs, the connection from you does not count, only their reciprocation off that edge.