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Connecting the Dots

Can the tools of graph theory and social-network studies unravel the next big plot?

Brian Hayes

Plotting the Plotters

What do the principles of social networks and graph theory tell us about the structure of terrorist cells? The very word "cell" offers a clue: It suggests compartmentalization. And indeed the lore of spy rings and resistance fighters speaks of limiting communication so that if one person is captured others will not be put in jeopardy. At the same time, however, the members of the group have to keep in touch in order to make plans and carry them out.

An illuminating case study comes from a rather different context: price-fixing by manufacturers of electrical equipment in the 1950s. The social network of the colluding managers and executives was examined by Wayne E. Baker of the University of Chicago and Robert R. Faulkner of the University of Massachusetts. They found that "the structure of illegal networks is driven primarily by the need to maximize concealment, rather than the need to maximize efficiency." Nevertheless, the price-fixing and bid-rigging simply could not be accomplished without communication among the conspirators, especially in the case of the biggest machinery. Despite the risks, executives had to meet face-to-face to coordinate their plans.

Networks of terrorists apparently face the same conflicting imperatives. Valdis E. Krebs, a consultant who usually applies social-network analysis to business problems, has used the same tools to map relations among the September 11 hijackers. In a paper written just a few weeks after the attacks, he found the network surprisingly sparse. Although every hijacker could be connected to every other via some path through the network, many of the paths were quite long, passing through three or four intermediaries. This attenuated structure would make communication extremely inefficient.

Krebs later revised his analysis, as more information became available. He has posted a new map at the Web site Here he reaches a different conclusion. Starting with two men who were already under suspicion in January of 2000, Krebs finds that known linkages lead to all 19 hijackers, and to other conspirators as well. Each node of the network is tied to the two initial subjects either directly or through a single intermediary.

José A. Rodríguez of the University of Barcelona has created a similar network map for the bombing of commuter trains in Madrid on March 11, 2004. Rodríguez recorded several kinds of strong links among the conspirators. Some had ties of kinship or had been childhood friends; others congregated at a shop owned by two of the subjects; some were veterans of earlier wars or terrorist actions. Looking at just the 13 men who actually placed and detonated the explosives, Rodríguez found that the strong ties produced a somewhat strange network. A core of six people formed a clique: Each one was linked to all the others. But the remaining members were only loosely associated or were completely disconnected from the main group.

The outlook changed entirely when Rodríguez included some 70 persons associated with the plot in various ways and when he mapped weak ties as well as strong ones. The weak ties denote pairs of people connected by financial transactions, casual encounters and the like. This larger and fuller network looks much like what Granovetter's theory would predict. There are several dense clusters, within which most nodes are strongly connected, but the clusters communicate with one another only via comparatively loose and unreliable couplings. For example, one cluster is made up of Spanish citizens from whom the bombers obtained explosives; most paths from this subgroup to the rest of the network pass through a single node, a vulnerable choke-point.

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