Cutting costs: Sustainability matters even in complex networks

North­eastern researchers revealed just such a mea­suring strategy in a new paper pub­lished in Nature Physics.

"We pro­vide a metric--called 'con­trol energy'--to char­ac­terize the amount of effort needed to con­trol real-world com­plex sys­tems," says first author Gang Yan, a post­doc­toral research asso­ciate in Northeastern's Center for Com­plex Net­work Research, which is directed by Albert-Laszlo Barabasi, Robert Gray Dodge Pro­fessor of Net­work Sci­ence and the paper's cor­re­sponding author.

These self-organized net­works, unlike an engi­neered one under your car's hood, include cel­lular net­works, social net­works, and mobile-sensor net­works. That makes poten­tial appli­ca­tions of Yan's metric wide-ranging: from helping to iden­tify key points in the meta­bolic path­ways of bac­te­rial cells that new drugs might target to deter­mining the most crit­ical areas to mon­itor and pro­tect in an online secu­rity system.

"Esti­mating the con­trol energy, or effort, is key in exe­cuting most con­trol appli­ca­tions, from con­trol­ling dig­ital devices to under­standing the con­trol prin­ci­ples of the cell," says Barabasi. "These results have mul­tiple appli­ca­tions in many dif­ferent domains where con­trol of the net­work becomes a key objective."

A net­work com­prises points of con­nec­tion, or "nodes"--individual units, such as a metabo­lite, a gene, a person, or even a gas pedal--and the links or inter­ac­tions tying those nodes to one another. "Driver nodes" are the select nodes that net­work admin­is­tra­tors zap with external sig­nals in order to con­trol the system. The con­di­tion of a driver node--for example, a gene coding a pro­tein or a person expressing his opinion about a polit­ical candidate--evolves over time as a result of both the node's internal dynamics and how it con­nects with its neighbors.

Pre­vious studies of the con­trol mech­a­nisms of com­plex sys­tems focused on iden­ti­fying these driver nodes, says Yan. His finding goes fur­ther, enabling a kind of net­work cost-benefit analysis. With it, net­work sci­en­tists could iden­tify not only the min­imum number of driver nodes to target for input sig­nals but also the "cheapest," most energy-efficient ones.

"It would be extremely dif­fi­cult to con­trol a large net­work by inputting sig­nals to only one driver node," says Yan. "But it's not prac­tical to input sig­nals to all the nodes--that would take a huge toll on the system. Our finding pro­vides a way to make a tradeoff between the number of driver nodes and the cost of con­trol­ling the system."

Barabasi, who co-authored a break­through Nature paper describing an algo­rithm to ascer­tain the number of driver nodes required to con­trol com­plex net­works, points to the impor­tant insights of Yan and his col­leagues in the appli­ca­tion of control.

"Most net­works are not func­tional if they cannot con­trol them­selves," he says. "Indeed, that need for con­trol deter­mines the system's archi­tec­ture, whether the net­work is a brain, a cell, or a tech­no­log­ical system. A key ques­tion in this process is the amount of effort needed to con­trol the system. The paper by Yan and his col­leagues offers fun­da­mental results on this sub­ject, by showing that moving a system in some direc­tions can be easy, but in others can be excru­ci­at­ingly dif­fi­cult or costly."