SIX DEGREES

One of its young pioneers explains the rudiments of network theory, a science almost too new to have a name.

As an example of the complexity of networks, Watts (Sociology/Columbia Univ.) takes the 1996 western US power-grid failure, caused largely by the very safety features meant to prevent a blackout. The nature of a network is determined not by its individual members, the author reminds us, but by their connectedness. The title alludes to the proposition that each of us could communicate to anyone else on earth with no more than six intermediate steps—preposterous at first glance, considering that most of us stay within a small circle of acquaintances. But, as Watts points out early on, even a small degree of randomness in the network, such as one neighbor with out-of-town friends, makes for a high degree of interconnectedness among its parts. He details the research by mathematicians, biologists, physicists, and others that has led to the understanding that networks, whether of people, computers, or even the neural cells of nematode worms, have structural features in common. And while one might sneer at the insights of physicists into human behavior, a key breakthrough in network theory was the recognition that certain structures are universal. The mechanism that starts a large crowd clapping in unison without any signal also lets all the crickets in one meadow synchronize their chirping. Computer viruses spread in much the same way as the flu. Watts smoothly combines a historical survey of the field with real-world examples, often drawn from his personal experience. An extensive bibliography, graded by degree of mathematical sophistication, will be useful to those readers interested in pursuing the subject further.

Well-done, comprehensive overview of a field that’s likely to be an important growth area of science.