You’re dri­ving down the highway in your Honda Civic. You press the pedal to the metal and the speedometer flips to 90 as you torque into the fast lane. How much effort have you, and the car, expended?

No, this is not a pop quiz in a physics class.

It’s an example of how, every day, we expend energy when we con­trol the net­works in our lives—in this case, a net­work whose com­po­nents include the car’s accel­er­ator, steering wheel, and brake. Knowing how much that effort “costs” can help deter­mine which com­po­nents to manipulate—and to what degree—to ensure the smoothest, safest ride as you acclerate from 55 to 90 miles per hour.

On Monday, 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-​​László Barabási, 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 Barabási. “These results have mul­tiple appli­ca­tions in many dif­ferent domains where con­trol of the net­work becomes a key objective.”

The evo­lu­tion of a network

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.”

Barabási, 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.”

Geor­gios Tsekenis, now a post­doc­toral research fellow at Har­vard Uni­ver­sity, is the paper’s co-​​first author. Researchers Baruch Barzel, Jean-​​Jacques Slo­tine, and Yang-​​Yu Liu from Bar-​​Ilan Uni­ver­sity, the Mass­a­chu­setts Insti­tute of Tech­nology, Har­vard Med­ical School, and the Dana Farber Cancer Insti­tute, respec­tively, also con­tributed to the paper.