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Technology and Culture 45.1 (2004) 162-167



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Nodes, Links, and Phase Transitions
Popularizing "Network Science"

Greg Downey


In the wake of financial crises, infectious disease epidemics, cascading power failures, frustrating Internet slowdowns, and infrastructure-based terrorist attacks of the early twenty-first century, governments and private organizations alike have mustered experts from many different disciplines to search for new patterns, new explanations, and even new "natural laws" that can be brought to bear on the political, economic, and social risks of maintaining a globally connected and technologically dependent society. But even before the turn of the millennium, many of these experts had already coalesced under a new research agenda they dubbed "network science." Grown out of the spaces between mathematics, computer science, sociology, physics, and biology, and purporting to provide new insight into any sort of aggregate phenomena that might be conceptualized under a language of nodes, links, and phase transitions, network science has now reached a sort of critical state of its own: the first wave of popularization has begun.

The three books reviewed here—Albert-László Barabási's Linked: The New Science of Networks (Cambridge, Mass.: Perseus, 2002, $26), Mark Buchanan's Nexus: Small Worlds and the Groundbreaking Science of Networks (New York: W. W. Norton, 2002, $25.95), and Duncan Watts's Six Degrees: The Science of a Connected Age (New York: W. W. Norton, 2003, $27.95)—make up an interesting network of their own. Two of them (Linked, Six Degrees) were authored by key network science practitioners themselves. Two (Nexus, Six Degrees) were published by the same firm only a year apart. And two (Linked, Nexus) feature dust-jacket blurbs by another network science pioneer, Mark Granovetter. What all three works share is a sort of internalist narrative that mixes a bit of scientific history, a bit of conceptual explanation, and a bit of real-world relevance to convince the [End Page 162] reader that, as Buchanan puts it, "Networks that have grown up under different conditions to meet markedly different needs turn out to be almost identical in their architecture" (p. 15). The implicit claim that follows, for all three authors, is that the new science of networks is really worthy of such a title. Within this structure, all three books cover the same basic story. For one reason or another, in the early 1990s several independent research teams each decided to investigate the so-called small-world phenomenon defined by the 1960s chain-letter experiments of Stanley Milgram, expanded by the 1970s investigations of Mark Granovetter on "the strength of weak ties," and popularized in the 1990s play by John Guare titled Six Degrees of Separation.

In a small-world network, individual nodes (persons, in this case) are connected to others (socially acquainted) in such a manner that between any two nodes there exists a "short" path linking those nodes together. Milgram, exploring the number of intermediate hands a mailed letter would have to pass through, acquaintance by acquaintance, in order to connect two randomly selected correspondents who did not themselves know each other, came up with an average "social distance" of 5.5 persons in the 1960s; Granovetter, exploring how people found jobs through networks of social contacts, found that weak ties of acquaintance would more quickly generate new information than strong ties of friendship in the 1970s. The first question for the nascent network science, then, was: How do such small-world social networks work? The answer was rooted in the "random networks" theorized by Paul Erdös and Alfréd Rényi in the 1950s: if nodes are assumed to be randomly linked together, the resulting networks can be shown to have certain structural properties that can be described (statistically, on average) by certain mathematical formulas.

But random networks are not small-world networks (and, furthermore, human social networks of the six-degrees variety are clearly not random networks). To achieve small-world status, researchers found, a network needed to have one of two properties. A small-world network might be randomly clustered, as Watts and...

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