To illustrate his point, Barabasi uses the famous game, “Six Degrees of Kevin Bacon,” in which the second-tier movie star can be linked with almost any other actor in a couple of simple steps. Charlie Chaplin, for example, was in A King in New York with Robert Arden, who was in Little Shop of Horrors with Steve Martin, who was in Novocaine with Bacon himself.

The implications of the Kevin Bacon game may seem a little ho-hum, but after Barabasi explains the early mathematical debates over networks, Linked gets really interesting, showing how this new science promises to change the way we conduct everything from medical treatment to the war on terrorism.

For years, researchers assumed that networks operated through what statisticians call “normal distributions,” with an average, or mean, and a bell curve around that average. Human height, for instance, follows normal distribution, as most people are between five and six feet tall, with a few taller and a few shorter.

But now we know that networks are often organized in what statisticians call “power distributions,” with most data points clustered together at a low level, with a few out on the extreme. If height followed a power distribution, most people would be very short, but numerous 100-foot-tall men and women would wander the streets, and at least one 8,000-foot-tall man would work somewhere as a window-washer.

The result of this distribution is that the hubs (the really tall people) play a dramatic role in linking things together. On the Web, for example, Barabasi has found that browsers can get from pretty much any page to any other through about 19 links. That number is so low because a few sites such as Yahoo! can lead almost anyplace, even though a vast majority of Web pages have three or fewer links connecting to them.

The same is true of human beings socially. Most people have a core group of friends, but a few extraordinary connectors know thousands of other people and can link them all together. Malcolm Gladwell illustrated this point in his famous New Yorker essay “Six Degrees of Lois Weisberg.” Just as linkages between people in Chicago often pass through uber-socialite Lois Weisberg, Washington connections seem to flow through Vernon Jordan (remember his role in the Lewinsky scandal?).

Over the last few years, Barabasi has shown that a number of other systems work the same way. Gaetan Dugas, the so-called “Patient Zero” who had sex with thousands of men in the early 1980s, was a hub for spreading AIDS. A tumor-suppressing gene named P53 serves as a network hub that controls a large number of proteins in the human body. Paul was a hub for spreading Christianity.

Not only do these hubs serve as the core for current networks, they also tend to grow stronger over time. When Google became the search engine of choice, more people started to link to it. Vernon Jordan is in demand because of all the people he already knows. This phenomenon ensures that networks retain their essential character as they grow.

Barabasi’s research has some profound implications. For one, these types of networks are extremely resistant against random attacks or failures. Eliminate one Web site out of every five, and enough interlinking tentacles will remain to keep the network functional.

But at the same time, the existence of such powerful hubs makes networks extremely vulnerable to targeted attacks. Knock out Yahoo! and the Web would be vastly harder to navigate. When an Oregon power line exploded in 1996, it brought down the country’s electricity distribution from the Rockies to the Pacific.

Targeted attacks also have the potential to be used for good. In theory, forcing Dugas to use condoms 20 years ago might have attenuated the AIDS crisis. If al Qaeda works the way that most networks do, getting rid of its hubs–Osama bin Laden, Ayman Al-Zawahiri, and Mohammed Atef–might destroy it.

Linked bounces from story to story in short snippets, and sometimes feels like a 250-page “Tilting at Windmills” column, but it’s still very lucid by the standards of scientific exposition. More important, it matters. Looking at biological networks is one of the fastest-growing fields in medicine, for example, and the world’s financial, agricultural, and economic structures grow more connected by the day. There’s a lot to learn from Kevin Bacon and Vernon Jordan–and Barabasi has written an important guidebook.

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