Intermediate (small-world) network

important. But the fact that you needed very few shortcuts to make the network world small implied that small-world networks might be common in nature. Watts and Strogatz tested that possibility on three real-world examples: the film actors’ network starring Kevin Bacon, the electrical power grid in the western United States, and the network of nerve cells in the tiny roundworm C. elegans.5 In all three cases, these networks exhibited the small-world property, just like the models of hypothetical networks that were intermediate between regular and random.

“Thus,” Watts and Strogatz concluded, “the small-world phenomenon is not merely a curiosity of social networks nor an artifact of an idealized model—it is probably generic for many large, sparse networks found in nature.”6

If so (and it was), Watts and Strogatz had opened a new frontier for mathematicians and physicists to explore, where all sorts of important networks could be analyzed with a common set of tools. In just the way that statistical physics made it possible to tame the complexities of a jumble of gas molecules, mathematicians could use similar math to compute a network’s defining properties. And just as all gases, no matter what kinds of molecules they contained, obeyed the same gas laws, many networks observed similar mathematical regularities. “Everybody pointed out, isn’t this remarkable that these totally different networks have these properties in common—how would you have ever thought that?” Strogatz said.

Several network features can be quantified by numbers analogous to the temperature and pressure of a gas, what scientists call the parameters describing a system. The average number of steps to get from any one node to any other—the “path length”—is one such parameter. Another is the “clustering coefficient”—how likely



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