By Shaun Hendy 30/09/2009

A new mobile phone network called ’2degrees’ was launched in New Zealand earlier this year. As explained in its advertising campaign (fronted by the excellent Rhys Darby from Flight of the Conchords), the name alludes to the (alleged) only two degrees of separation between New Zealanders, as opposed to the six degrees that separate the rest of the world. Are Kiwis really so well connected?

The idea that people are separated socially from one another by at most six degrees has been around for a hundred years or so. Psychologist Stanley Milgram put it to the test in the late 1960s, using a chain-letter approach to delivering mail. Rather than addressing the letter directly to the intended recipient, Milgram sent the letter to a randomly selected intermediate, giving them the final recipient’s name and city, but not full address. He then asked the intermediary to send the letter on to a friend who they thought might be able to get it closer to its final target. The goal was to discover the number of social links that were needed to connect two people selected at random within the United States.

Although most of Milgram’s letters never reached their destination, those that did took on average only six links to be delivered. Hence the ’six degrees’ that supposedly separate us all.

With the arrival of the internet, these sorts of experiments have become much easier to conduct. You can play a similar game yourself at the Oracle of Bacon, a site which searches imdb to find the number of co-starring relationships that separate any actor from Kevin Bacon. Rhys Darby has a Bacon number of two: he co-starred in ’Yes Man’ with Albert Miranda, who in turn co-starred with Bacon in ’Frost/Nixon’. The average Bacon number in the database is just under three, and the average Darby number is roughly three and a half.

Both the Oracle of Bacon and Stanley Milgram’s experiment illustrate that individuals within large social networks are connected by relatively short paths. Not all networks are ’small’. Think of your family tree:  to follow your tree to your cousin, you’ll need four links (I hope) i.e. you to your parent to your grandparents to your aunt (or uncle) to your cousin. That’s already more than the average Bacon number, and in a network that only contains your extended family. Of course, you probably have direct social links with your cousin — this illustrates that social networks are different in structure to family trees.

Networks in which two individuals selected at random can be connected by a relatively small number of links are called small world networks. There are several popular books that discuss the science and mathematics of small world networks — I can recommend Six Degrees by Australian physicist turned sociologist Duncan Watts.

Scientists have identified other small world networks, including the internet and the world wide web. As I discussed in an earlier post, my research group has looked at networks of inventors. Networks of inventors turn out to be almost, but not quite, small world networks. Let’s call them medium world networks for now. They also share some features in common with the hyperlink structure of the web. But most interesting is that some of their properties do depend on network size, i.e. the properties of your collaborative network depend on the number of people in the network. This has implications for a small country like New Zealand — I’ll discuss this further in a later post.

So … are New Zealanders separated socially by only two degrees? Actually, a quick scribble on the back of the envelope suggests to me that it’s about four and a half: ’4.5degrees’ is not quite as catchy for a phone company, although it does conjure up an image of somewhere slightly warmer (possibly planet Earth by 2050). Still, I usually tell my students not to worry too much about factors of two, so I guess I can live with the ’2degrees’ ads provided they carry on being funny. Perhaps someone would like to design a Kiwi Milgram test to measure this …  how many links separate you from Rhys Darby?

0 Responses to “2degrees?”

  • But does the fact that most of the letters in the original experiment were never delivered suggest that while when links exist that there may be only 6 degrees, some people are just never connected with others i.e. an infinite degree?

    • “But does the fact that most of the let­ters in the orig­i­nal exper­i­ment were never deliv­ered sug­gest that while when links exist that there may be only 6 degrees, some peo­ple are just never con­nected with oth­ers i.e. an infi­nite degree?”

      Interesting question. I suspect the failure rate says a lot about people’s willingness to participate in unsolicited psychology experiments, but if you check out the Stats NZ report above you’ll see that almost all NZ employees are connected, so it would be very surprising if there were unconnected social components out there. On the other hand, who would know … 🙂

      There is another property of social networks that come into play in the Milgram experiment: your social network must be searchable in some way. That is, you need to have some idea of who in your social network might be closer to the target than you are. Obviously in this case, geography plays some role. I may post on this in more detail at a later date.