Linked: The New Science of Networks (review)

All the world's a network—at least if the contemporary pervasiveness of web and network metaphors is anything to go by. In fact, the comparison in itself isn't even especially new.As Laura Otis has shown in Networking (2001), scientists, engineers, and fiction writers have intuited the prevalence of networks in various complex systems, from the human body to modern societies, since at least the invention of the electric telegraph in the mid-19th century. But the rapid growth of the Internet, in particular the World Wide Web, in the 1990s has made questions about the properties and prevalence of networks virtually inescapable. More importantly, it has also provided a fascinating new network to map and investigate. And many networks, including the Web, have turned out to possess a number of crucial traits that are both characteristic and amenable to study.

University of Notre Dame Physics professor Albert-László Barabási is part of a group of researchers analyzing the structure and properties of real networks who have recently found similar laws governing systems that range from Swedish dating habits, Hollywood casting, and corporate organization, to living cells, ecosystems, and the Internet. In Linked, Barabási provides a highly accessible report from the frontlines; most of the research he discusses in his main chapters was undertaken within the last four years. While some readers may find his first-person account distracting or self-aggrandizing (he reports that a paper he wrote on a transatlantic flight was soon published in Science), others will appreciate—as I did—the sense of having such a direct connection to new research.

Barabási pays tribute to Paul Erdös and Alfréd Rényi's pioneering mathematical explorations of randomly linked networks some 40 years ago. But he points out that these elegant theoretical models face a problem if we try to import them into the real world: in most real networks, links don't seem random—whether they are hyperlinks from personal Web pages to a popular site or collaborative links between researchers and a brilliant, industrious colleague (for instance, Paul Erdös). This difference has important consequences. In a random network, we can speak of a "typical" node and plot the number of links each node has as a graph with a peak in the middle (this average number of links per node is its "scale"). But in the nonrandom networks Barabási explores, the apportionment of links follows a power law, a distribution pattern familiar from research on complexity and self-organization. In these networks, there is no bell curve, no typical node. Most nodes have only a few links, but a small number of nodes turn out to be hubs with many links. Such hubs provide the principal connection between many parts of the network. Consequently, it makes little sense to analyze the average number of links per node; these networks are "scale-free."

What is the explanation for the emergence of scale-free networks? Well, for one thing, they have been produced by growth (for instance, the sensational growth of the Web in the 1990s), a process that rewards the oldest nodes, which have had the most chances to receive new links. But Barabási and his colleagues have found that network growth alone isn't sufficient to explain the characteristic power-law distribution of links. In addition to growth, Barabási suggests that new links demonstrate preferential attachment. That is, the more links a node already has, the more new links it will get: the rich get richer. Other effects (for example, the expiration of old links) may alter the number or size of hubs, but in general, as long as growth and preferential attachment are present, scale-free networks with hubs and power-law distributions will emerge. Add a factor for "fitness" in a competitive environment—for instance, the fact that most...