Wikipedia, itself a text version of a small world, describes a small-world network as “a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps”. Understanding how examples of these networks connect nodes so efficiently holds the promise of revolutionizing how we think about viruses (both digital and biological), cancer, neurology, bird flu and HIV dissemination, and international finance networks, to touch on just a few areas of interest.
Image: Internet Domain Routes by J. Evans
But what about networks of networks? Does small-world network science have anything to say about the relatively recent phenomenon of social network aggregation, where membership of a fairly innocent-looking Web 2.0 net such as Facebook could see you included in a vast universe of other social nets?
Connecting to other social networks seems to follow an “opt in” model, on the surface, at least. The implication is that you will only be aggregated in other nets if you choose to be, but this is unlikely to always be the case. It’s well known, for example, that credit organisations share information about their customers, including risk assessments, credit histories and other profiling information, all of which can adversely affect the customer’s ability to borrow money, buy a car, or start a business. That’s a very powerful form of networking when you think about it, and its exploitation has probably been responsible for much of the world’s current financial crisis.
Proprietary social network aggregators such as Gathera let you “bring all your online accounts that you frequently check together into one place – the IE browser sidebar” (note the proprietary browser they seem to be endorsing). Gathera also supports a range of communication nets such as MSN, Twitter, Flickr, Googletalk and Facebook Chat.
Pioneers of network science Duncan Watts and Steven Strogatz have published several papers since the late 90s that explore the connectivity of networks at a mathematical level. A seminal paper published by Watts and Strogatz in Nature (1998) is titled “Collective dynamics of ‘small-world’ networks“. It explores the idea that simple networks can be re-wired to “introduce increasing amounts of disorder” that can be “highly clustered, like regular lattices, yet have small characteristic path lengths”. That is, the number of path journeys required to connect disparate nodes in the system is surprisingly short, hence the “small-world” analogy. This insight is sometimes characterised as the Six Degrees of Kevin Bacon phenomenon, after a trivia game invented by three college students from Albright College in Reading, Pennsylvania that shows any Hollywood actor can be connected to Kevin Bacon through common film links in a maximum of six steps. A Bacon Number is allocated to anyone connected to KB as a measure of the number of steps. Kevin himself has a Bacon Number of 0.
The value in exploring social and other networks in this way is only now beginning to be realised, in a large range of research fields. Albert Barabasi, another pioneer in this field has looked at error tolerance in complex networks from a small-world perspective. A key publication of his, Linked: The New Science of Networks (2002) discusses the critical importance that hubs play in any small-world network. If you wanted to stop the dissemination of avian flu through a country, for example, the best strategy would be to protect the main communicative hubs in the network; the international airports. If these were breached, it would be virtually impossible to prevent a pandemic spread of the virus through the community. The same approach has been applied to the study of a large range of human diseases as a small-world network. Researchers track the connections between apparently unconnected diseases to determine how having one disease might promote the contraction of other diseases, or, conversely, might offer protection from them.
Network science has been characterised as a key science of the 21st century and it’s certainly making an impact on many research areas. If you link to this blog, you’re already part of the system.
UPDATE: 19/11/08 – You can view the program “How Kevin Bacon Cured Cancer”, which features several of the researchers mentioned above, by streaming it from the ABC Website. Go to: http://www.abc.net.au/tv/documentaries/interactive/futuremakers/ep4/.
For an interesting discussion on this documentary visit the Edge Foundation’s website at http://www.edge.org/ . Their mission is “to promote inquiry into and discussion of intellectual, philosophical, artistic, and literary issues, as well as to work for the intellectual and social achievement of society.” Some interesting people who have presented at Edge seminars, or at it’s predecessor, the Reality Club, include; Daniel Dennett, Richard Dawkins, Freeman Dyson, Niles Eldredge, Murray Gell-Mann, Stephen Jay Gould, Stewart Kauffman, Benoit Mandelbrot, Lynn Margulis, Howard Gardner, Steven Pinker, Roger Schank, Betty Friedan, Paul Krassner, Naomi Wolf, the late Abbie Hoffman, Ken Kesey, Steven Levy, and Mark Mirsky.