Connectivity in Random Networks Can Be Suppressed, but with Explosive Consequences


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.

The red points represent the formation of a super-connected group or "giant component" within a network. credit: Raissa D'Souza/UC Davis
The red points represent the formation of a super-connected group or "giant component" within a network. credit: Raissa D'Souza/UC Davis

Alternate Contact: Liese Greensfelder | 530.752.6101 lgreensfelder@ucdavis.edu

In 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.

In the classic model of random network formation, known as the Erdos-Re 500

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