I currently follow an online course on Coursera called “Social Network Analysis“. The course offers the models and theory that lies behind social networks, and in addition let’s you play with datasets on programmes like Gephi and NetLogo. I decided to share one of the ideas/concepts, because it was particularly interesting, also for people who are not that into social network analysis.
Small Worlds. Lada Adamic, the course instructor, starts with the well-known example of the letter chain experiment, conducted by Stanley Milgram in 1967. The idea behind it was that people in Nebraska and Kansas were asked to send a letter to a stockbroker in Massachusetts, through people who they thought knew people who could deliver the letter directly, or knew people who knew people etc…
It turned out that on average the length of the chain was about 6 — the widely known “six degrees of separation”.
(However, only about 20% of the letters reached their destination, due to someone in the chain not passing on the letter.)
Is 6 really that little? This where the idea of “what a small world we live in” comes in.
Researchers Pool and Kochen in 1978 established that on average a person has about 500 to 1500 acquaintances.
Lada shows us that even choosing the modest average of 500 acquaintances per person yields gigantic networks
- the size of the network of second degree acquaintances (the acquaintances of your acquaintances) is: 500^2 = 250 000
- the third degree is already: 500^3 = 125 000 000 (125 MILLION) people…
Just check your LinkedIn network. My relatively small number of connections nonetheless ‘gives’ me about 1.4 million 3rd degree connections.
With that in mind, that it takes 6 people to communicate from one state in the U.S. to another, seems to be quite high. There is a but to that. How can you be sure that these people actually choose the ‘shortest path’ — so choosing exactly those people who can make sure that the chain will not take any unnecessary steps? You don’t really know.
A team of researchers studies the degree of separation of 721 million Facebook users and this is what they find,
Using state-of-the-art algorithms developed at the Laboratory for Web Algorithmics of the Università degli Studi di Milano, we were able to approximate the number of hops between all pairs of individuals on Facebook. We found that six degrees actually overstates the number of links between typical pairs of users: While 99.6% of all pairs of users are connected by paths with 5 degrees (6 hops), 92% are connected by only four degrees (5 hops). And as Facebook has grown over the years, representing an ever larger fraction of the global population, it has become steadily more connected. The average distance in 2008 was 5.28 hops, while now it is 4.74.