n the life of many successful networks, the connections between elements increase over time. As connections are added, there comes a critical moment when the network's overall connectivity rises rapidly with each new link.
Now a trio of mathematicians studying networks in which the formation of connections is governed by random processes, has provided new evidence that super-connectivity can be appreciably delayed. But the delay comes at a cost: when it finally happens, the transition is virtually instantaneous, like a film of water abruptly crystallizing into ice.
The team's findings — described in a paper with an accompanying commentary in the March 13 issue of the journal Science —could be useful in a number of fields: from efforts by epidemiologists to control the spread of disease, to communications experts developing new products.
"We have found that by making a small change in the rules governing the formation of a network, we can greatly manipulate the onset of large-scale connectivity," said Raissa D'Souza, an associate professor of mechanical and aeronautical engineering at UC Davis.