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Book Review
Six Degrees of Separation

Linked: The New Science of Networks, by Albert-Laszlo Barabasi. Perseus Publishing, 2002, 280 pages, $26 (hardcover).

In the game "connect the dots," a picture emerges only when all of the dots are properly linked to form a meaningful network. Similarly, the familiar pastime "Six Degrees of Kevin Bacon"—based on the "Six Degrees of Separation" or "Small World" phenomenon—involves linking people to one another through their specific associations. Bela Lugosi has a "Bacon number" of 3. He was in Abbot and Costello Meet Frankenstein with Vincent Price (step 1). Price was in The Raven with Jack Nicholson (step 2). And Nicholson was in A Few Good Men with...Kevin Bacon (step 3). Albert Barabasi's fascinating new book Linked is about the pictures that emerge when any sort of real-world "dots" are connected—webpages, people in social networks, animals in food webs, or molecules in cells. He argues that all of these networks have similar features and that these features tell us how networks operate.

Barabasi's principle claim is that many networks are "scale-free." This property is best illustrated by two observations that the author made about the Internet. Barabasi first noticed that the Internet has a few webpages that are highly connected to other webpages (a la Kevin Bacon), whereas the majority of webpages have few such links. Thus the Internet is not a randomly connected network, in which the number of links per webpage would be similar. Second, Barabasi observed that the number of links per webpage follows a particular distribution called a "power-law." This means that no matter how large the web grows, there will still be the same average number of connections between any two webpages.

When Barabasi and his colleagues examined the network architecture of biological systems they observed something intriguing. The metabolic networks that convert nutrients into energy, networks of human sexual relations, protein-protein interaction networks in cells, and food webs describing which living things eat what are all "scale-free."

The scale-free network architecture of biological systems has profound relevance. The fact that average number of connections is constant, despite the size of the network, means that it is possible to go from one node to another in the same number of steps or time in both large and small networks. Consider the entire world's population rather than merely Hollywood. A scale-free network architecture means that Bela Lugosi and a dentist in Bangkok would have similar Bacon numbers, as if Kevin Bacon attended drama school with a Thai actor whose uncle is a dentist in Bangkok. Furthermore, "scale-free" networks resist being disrupted by random losses because the common, poorly connected nodes are more likely to be hit than a few, well-connected hubs. Losing a star of Kevin Bacon's stature destroys a film project. Not so losing one of many nameless extras from the production.

Such network properties have disquieting implications for the spread of diseases like HIV. If the average "sexual distance" between two people in the works is independent of the size of the population, then HIV will spread just as quickly in a large society as it does in a small society. Of even grater concern is the notion that treating individuals at random may not efficiently disrupt the spread of HIV. Instead, targeting the most connected individuals is predicted to stop the disease more quickly.

The full range of biological phenomena that fit the concepts Barabasi champions has yet to be determined. Is the "scale-free" property a universal feature of biological networks? Will knowledge of network properties of molecules inside cells help us control cancer? It will be interesting to learn the answers to these questions over the next few decades. In any case, Barabasi's immensely readable book provides an ideal introduction to the emerging science of networks.