Book Review: Linked : August 23, 2004

A highly recommended read is the book Linked: The New Science of Networks, by Albert-Laszlo Barabasi. I just finished reading this book and I can recommend it highly. It's a book on the relatively new science of network theory, written by one of the pioneering researchers in the field, but geared to the layperson who has an interest in networks (everything from the Internet to fashion fads to virus transmission). To give you a flavour, here's an extract comparing a power law to a bell curve:

If you are not a physicist or mathematician, most likely you have never heard of power laws. That is because most quantities in nature follow a bell curve...For example, if you were to measure tha height of all your adult male acquaintances and prepare a histogram counting how many of them are four, five, six, or seven feet tall, you will find that most people in your sample are between five and six feet tall. Your histogram wil have a peak around those values. Indeed, unless you hang out with a lot of basketball players, you will have very few seven or eight-foot people in your sample. The same is true for shorter people: Three or four-foot tall individuals are rather rare...

In the past few decades scientists have recognized that on occasion nature generates quantities that follow a power law distribution instead of a bell curve. Power laws are very different from the bell curves describing our heights. First, a power law distribution does not have a peak. Rather, a histogram folowing a power law is a continuously decreasing curve, implying that many small events coexist with a few lare events. If the heights of an imaginary planet's individuals followed a power law distribution, most creatures would be really short. But nobody would be really surprised to see occasionally a hundred-foot monster walking down the streest. In fact, among six billion inhabitants there would be at least one over 8,000 feet tall. (p. 67)

The power law theorem applies to Web sites on the Internet: the majority of Web sites are pointed to by only a small number of other Web sites, but a small handful of sites (e.g. eBay, Yahoo!, Google) are pointed to by hundreds of thousands, even millions of Web sites.

Later on in the book the author also describes the HIV infection epidemic as yet another curve following a power law: a lot of men have a small-to-medium number of sexual partners, but a small number of men have an extremely high number of sexual partners, and can therefore potentially transmit the HIV virus to a lot of people (e.g. Gaétan Dugas, the promiscuous Montréal airline attendant who worked for Air Canada who had previously been considered by some epidemiologists as "Patient Zero" in the AIDS epidemic, based on a 1984 study published in The American Journal of Medicine (that theory has since been disputed and discredited by many other epidemiologists).

What's very surprising to me is that most of the theory behind networks has only been developed within the past decade, with the Internet providing a prime "laboratory" for researchers to study.