Networks that are resilient on their own become fragile and prone to catastrophic failure when connected, suggests a new study with troubling implications for tightly linked modern infrastructures.

Electrical grids, water supplies, computer networks, roads, hospitals, financial systems – all are tied to each other in ways that could make them vulnerable.

"When networks are interdependent, you might think they're more stable. It might seem like we're building in redundancy. But it can do the opposite," said Eugene Stanley, a Boston University physicist and co-author of the study, published April 14 in Nature.

Most theoretical research on network properties has focused on single networks in isolation. In reality, many important networks are tied to each other. Anecdotal evidence – the crash of communications networks (.pdf) in lower Manhattan after 9/11, the plummeting of markets around the world after the Black Monday stock market collapse of 1987 – hints at their fragility, but the underlying mathematics are largely unexplored.

The Nature researchers modeled the behavior of two networks, each possessing what's known as "broad degree distribution": A few nodes have many connections, some have an intermediate amount of links and many have just a few. Think of the networks as having only a few hubs, but many spokes. On their own, such networks are known to be stable. A random failure is likely to disable a leaf, leaving the rest of the network's connections mostly intact.

In the new study, the researchers connected two of these networks. While many node failures were required to crash the networks when they were independent, a few failures crashed the networks when they were linked.

"Networks with broad distributions are robust against random attacks. But we found that broad interconnected networks are very fragile," said study co-author Gerald Paul, a Boston University physicist.

The interconnections fueled a cascading effect, with the failures coursing back and forth. A damaged node in the first network would pull down nodes in the second, which crashed nodes in the first, which brought down more in the second, and so on. And when they looked at data from a 2003 Italian power blackout, in which the electrical grid was linked to the computer network that controlled it, the patterns matched their models' math.

That broad networks could be so fragile is surprising, but even more important is how rapidly the crash happened, with sudden catastrophic collapse instead of a gradual breakdown, said Indiana University informaticist Alessandro Vespignani in a commentary accompanying the paper. "This makes complete system breakdown even more difficult to control or anticipate than in an isolated network," he wrote.

According to Raissa D'Souza, a University of California, Davis mathematician who studies interdependent networks, the findings are "a starting point for thinking about the implications of interactions."

D'Souza hopes such research will pull together mathematicians and engineers. "We now have some analytic tools in place to study interacting networks, but need to refine the models with information on real systems," she said.

Research into linked systems could help engineers build more resilient networks, or identify existing weaknesses. At the very least, they stress the importance of preparing for sudden, catastrophic failures. "We must recognize the possibility of big disasters, and take steps to prepare," said Stanley, noting how unprepared political and economic leaders were for the financial collapse that triggered the current recession.

"These stories underscore that when trouble happens, we're surprised. But we shouldn't be," said Stanley.

Image: From left to wright, a failure cascades through an Italian power network (overlaid on the map) and the internet nodes that depend on it (above the map)./Nature.

See Also:

Citations: "Catastrophic cascade of failures in interdependent networks." By Sergey V. Buldyrev, Roni Parshani, Gerald Paul, H. Eugene Stanley & Shlomo Havlin. Nature, April 15, 2010.

"The fragility of interdependency." By Alessandro Vespignani. Nature, April 15, 2010.

Brandon Keim's Twitter stream and reportorial outtakes; Wired Science on Twitter. Brandon is currently working on a book about ecological tipping points.