In 1736 the Swiss mathematician Leonhard Euler ended a debate among the citizens of Königsberg, Prussia, by drawing a graph. The Pregel River divided the city, now Kaliningrad, Russia, into four sections. Seven bridges connected them. Could a person cross all seven without walking over the same one twice?
Euler began with a map that cleared away everything—the homes and streets and coffeehouses—irrelevant to the question at hand. Then he translated that map into something even more abstract, a depiction not of a physical place but of an interconnected system. The four sections became dots, and the seven bridges became lines. By transforming Königsberg into simple nodes and edges (as mathematicians have come to call such abstractions), Euler could subject the system to mathematical analysis. In doing so, he proved that a person could not cross all seven bridges without walking over the same one twice. More important, he mapped a network for the first time.
Over the next two centuries, scientists built on Euler’s work to develop graph theory, a branch of mathematics that would eventually serve as the basis for network science. But it wasn’t until 1959—when the Hungarian mathematicians Paul Erdös and Alfréd Rényi proposed a means by which complex networks evolve—that a defined theory of networks began to emerge. And it was only in the mid-1990s that scientists began to apply that theory to really complex problems. Before then, large data sets were difficult to obtain and even more difficult to process. But as data became more accessible and processing power cheaper, researchers began applying graph theory to everything from protein interactions to the workings of the power grid.
Albert-László Barabási, a Romanian-born physicist at the University of Notre Dame, was one of those researchers. In the past decade and a half, he has transformed the way his colleagues understand networks at least twice. His theories have influenced important developments in engineering, marketing, medicine and spycraft. And his research may soon allow engineers, marketers, doctors and spies to not just understand and predict network behavior, but also to control it.
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