A kid in a network shop

by Angela Herring

“There are some ques­tions that you don’t need to be a sci­en­tist to ask. You need to be a little kid,” said Baruch Barzel, a post-​​doctoral research asso­ciate at Northeastern’s Center for Com­plex Net­work Research.

Two-​​and-​​a-​​half years ago, when he joined the lab led by world-​​renowned net­work sci­en­tist Albert-​​László Barabási, these were the ques­tions that intrigued Barzel. In a paper recently released in the journal Nature Physics, Barzel and Barabási have answered them.

Com­plex net­works, Barzel explained, like those of genetic, bio­chem­ical, or even social inter­ac­tions, all share the same struc­tural fea­tures. For example, they all obey some­thing called the “small world phe­nom­enon,” where every node is con­nected to every other node by a sur­pris­ingly small number of steps. They also all have a high degree of het­ero­geneity, where a few nodes are unex­pect­edly much more con­nected than the majority.

When Barabási’s team iden­ti­fied this ele­ment of uni­ver­sality common among the struc­tures of com­plex net­works, it laid the foun­da­tion for an entirely new field of research: net­work sci­ence. But Barzel wanted to take this fur­ther. “So what if these com­plex net­works have the same struc­tures. Does that mean that they’ll have the same behavior?” he wondered.

When Barzel joined Barabási’s lab, he didn’t expect the answer to his ques­tion to be yes. “You take human beings and pro­teins and you con­struct the exact same net­work from the two enti­ties, why would you expect them to behave the same?” he said. “My feeling was some­thing was missing.”

A net­work con­sists of a bunch of nodes with links con­necting them, and they all look very sim­ilar regard­less of what the lines and dots rep­re­sent. “What doesn’t appear there,” said Barzel, “is the story behind the links.”

It’s that story—translating the con­nec­tion between two things into their influ­ence on each other—that is so impor­tant to moving from struc­ture to behavior.

For instance, recall those highly con­nected nodes. You might expect that a person con­nected to thou­sands of other indi­vid­uals will have a bigger impact on the net­work than a person only con­nected to 10 or 15 others. But if the highly con­nected indi­vidual has no influ­ence over his con­nec­tions, he won’t have much power to change the system.

In the new Nature Physics paper, Barzel explains that when he looked at the pat­terns of influ­ence rather than merely the struc­tural pat­terns, he found another level of uni­ver­sality that he did not expect. “I was aiming to find that once you account for dynam­ical behavior, every­thing is dif­ferent,” he said.

But in fact, while a net­work of pro­teins and a net­work of humans have dif­ferent micro­scopic behav­iors (pro­teins react with each other, humans talk with each other), they, and all other com­plex net­works, are forced to follow just one of a small set of dis­tinc­tive types of behaviors.

At the macro­scopic level, only a few of those micro­scopic details matter. And so with just a little bit of key infor­ma­tion about a par­tic­ular net­work, Barzel and his col­leagues are now able to make pre­dic­tions about how a system will behave under var­ious circumstances.

Originally published on news@Northeastern on September 25, 2013.

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