Airline networks are pretty much scale-free

You’ll be surprised to hear what a world-renowned physicist says about what kills creativity

by Todd Neff

In late 2016, Albert-Lászlo Barabási and colleagues published a paper aimed at putting empirical heft behind the anecdotal truism that physicists did their best work when they were young. They considered 2,887 of them, all the way back to 1893, analyzing “impact” papers by age of their progenitor. They found that younger physicists had more impact. But it was because the younger scientists wrote more papers. Age didn’t matter, they concluded.

“The bottom line is: Brother, never give up,” Barabási told the New York Times. “When you give up, that’s when your creativity ends.”

There’s a bit of irony in Barabási being involved in a paper fueling the professional hopes of the not-young. He had, as Albert Einstein and Marie Curie and many others before him, made enormous scientific contributions while still very young. Barabási, already a central figure in the invention and development of key aspects of modern network theory, had by 2000 earned himself an endowed chair at the University of Notre Dame. He was 32.

An ethnic Hungarian born in Transylvania, Romania, Barabási earned his master’s degree in Theoretical Physics at the Eötvös Loránd University in Budapest, and was awarded a PhD three years later (this is, for those unfamiliar with physics PhD work, ridiculously fast) at Boston University. A few years later, in 1995, he established the foundations for his grand, youthful achievement: establishing the theoretical foundations for — and identifying real-world examples of — scale-free networks.

Understanding the concept of a scale-free network is essential in grasping a great deal of Barabási’s work. The youthful World Wide Web was cited as a key example, back when it had a quaint 800 million pages (it’s somewhat larger these days). The idea is that scale-free networks don’t grow equitably. Rather, certain nodes grow enormous numbers of connections as the network expands while others don’t, leading to a sort of rich-get-richer scenario where your Wikipedias, Googles, major news sites and so forth gain disproportionately as the network blossoms. These hub sites’ linkages appear to be able to expand to endless degrees — to enormous, incalculable scales — and hence the “scale-free” name.

For a visual idea of what’s going on here, check out this graphic from an interesting 2007 piece Barabási wrote for IEEE Control Systems Magazine:

It contrasts random versus scale-free networks using the examples of U.S. road and airline networks. The distribution of a random (in this case road) network follows the bell-curve distribution above it, telling us that most nodes have the same number of links and that nodes with a large number of links don’t exist. So a random network is similar to a national highway network in which the nodes are the cities and the links are the major highways connecting them.

In contrast, the power-law distribution (top-right) of a scale-free network predicts that most nodes have only a few links held together by a few highly connected hubs. The U.S. airline network, in which a large number of small airports are connected to each other by means of a few major hubs, follows this law. So does, as mentioned, the Internet — as well as a host of other biological and social systems, Barabási and his colleagues have found.

Among the networks judged to be wholly or largely scale-free: Hollywood (actors and appearances in the same movie), cellular metabolism (molecules involved in burning food for energy participating in the same biochemical reaction), protein regulatory networks (interactions among proteins that help to regulate a cell’s activities), research collaborations (scientists co-authoring papers), sexual relationships (yowza!).

This all has rather huge implications. Once you’ve identified the fundamentals about how a network works, you can figure out how to break it (or protect it from others intent on breaking it) — which is of use to national security types, true, but also epidemiologists, as it turns out:

“Consider, for example, the need to eliminate bacteria by disrupting their molecular network or by vaccinating a few individuals in a population to break up the contact network through which a pathogen spreads,” he and co-author István Kovács wrote in the journal Nature.

What’s more, mapping out the human cell’s molecular networks could help research target drugs against “hub molecules” involved in certain diseases. In business, understanding the linkages within the financial system could help a repeat of the 2008 financial meltdown, or, conversely, help marketers propagate consumer buzz about their products, according to Barabási.

And so, nearly two decades after his epochal insight, Barabási is as active as ever, exploring the many tendrils of the field he launched, and the notion of giving up is clearly the last thing on his mind.

Albert-László Barabási is one of 60 masterminds slated for Brain Bar Budapest 2017. He’s part of a stellar lineup of the thinkers, creators, innovators, doers on tap to share insights with the more than 7,000 people attending this year’s festival, which is less than 60 days away!

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