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« Idolatry Redux | Main | Econ for Morons »

April 16, 2003

Culture and Scale-Free Networks


In the May issue of Scientific American, there is an article by Albert-Laszlo Barabasi and Eric Bonabeau on “Scale-Free Networks” that seems, to my mathematically ignorant eye, to have significant implications for the world of culture.

According to this article, the traditional way of studying networks assumed that they were like the U.S. highway system—that is, each node (major city) tends to be directly connected via superhighway to roughly the same number of other nodes. A few nodes had only one connection, most had four or five, a small number had as many as ten, but the number of connections per generally fit a “bell curve” with the largest number of nodes having a middling number of direct connections. (This is known, for reasons beyond my comprehension, as a “random” network.)

However, a different type of network (known as “scale-free”) has recently been widely studied, in which most of the nodes have a very low number of direct connections, and some of the nodes have a very large number of direct connections. This creates what is known as a “power law” distribution, as opposed to a “bell curve” distribution, and is the technical definition of what makes the two types of networks different. For us limited-math types, the key is the fact that the nodes with tons of connections function as hubs in scale-free networks.

An interesting example of such a scale-free network is the World Wide Web, where some pages are hyperlinked to (and from) zillions of other pages, while the vast majority of pages have few links. Examples of scale-free networks that have been studied in biology include cellular metabolism and protein interaction. But what, you say, does this have to do with 2Blowhards and our penetrating study of culture? Well, it so happens than many social networks are also scale-free, as Mssrs. Barabasi and Bonabeau report:

A collaboration between scientists from Boston University and Stockholm University, for instance, has shown that a network of sexual relationships among people in Sweden followed a power law: although most individuals had only a few sexual partners during their lifetimes, a few (the hubs) had hundreds. A recent study led by Stefan Bornholdt of the University of Kiel in Germany concluded that the network of people connected by e-mail is likewise scale-free. Sidney Redner of Boston University demonstrated that the network of scientific papers, connected by citations, follows a power law as well. And Mark Newman of the University of Michigan at Ann Arbor examined collaborations among scientists in several disciplines, including physicians and computer scientists, and found that those networks were also scale-free, corroborating a study we conducted focusing on mathematicians and neurologists.

[You've got to wonder how they divvy up the work in the social sciences, don't you? I mean, we've got a choice between studying the sex lives of Scandinavian blondes and the citation patterns among neurologists. Gee, which one would I chose?]

Assuming that artistic influence and prestige work in a scale-free manner (a hypothesis based entirely on my possibly shaky intuition), it might shed some light on many interesting aspects of our cultureverse. One such aspect is the emergence of art stars, the Shakespeares, the Michelangelos, and the Beethovens (as well as their contemporary equivalents). While in no way denigrating the artistic genius of these figures, they were (or are) in many cases surrounded by other extremely talented artists who do not have the same towering reputations today. Why did these individuals become “hubs?”

Turning to what has been learned from the study of scale-free networks, we can apply what is known about the emergence of such hubs in social networks. Two mechanisms have been identified. One is simple historical growth; for example, in 1990 the World Wide Web had only one page, while today it has over three billion. There is a fairly obvious tendency for nodes that are around when network growth starts to take off to become hubs. Second, there is a phenomenon known as preferential attachment, or the tendency to seek links to nodes that are either known or very well known. As Mssrs. Barabasi and Bonabeau put it:

When deciding where to link their Web pages, people can choose from a few billion locations. Yet most of us are familiar with only a tiny fraction of the full Web, and that sub set tends to include the more connected sites because they are easier to find. By simply linking to those nodes, people exercise and reinforce a bias toward them. This process of “preferential attachment” occurs elsewhere. In Hollywood the more connected actors are more likely to be chosen for new roles. On the Internet the more connected routers, which typically have greater bandwidth, are more desirable for new users. In the U.S. biotech industry, well-established companies such as Genzyme tend to attract more [joint venture] alliances, which further increases their desirability for future partnerships. Likewise, the most cited articles in the scientific literature stimulate even more researchers to read and cite them, a phenomenon that noted sociologist Robert K. Merton called the Matthew effect, after a passage in the New Testament: “For unto every one that hath shall be given, and he shall have abundance.”

Growth and preferential attachment clearly encourage the existence of hubs. When new nodes appear, they connect to the more connected sites, and these hot nodes develop more links than their less connected neighbors. And this “rich get richer” process also favors the first artists to develop reputations in new spaces—the Mannerist nude in the case of Michelangelo, the Elizabethan theater in the case of Shakespeare, Romantic music in the case of Beethoven. Thus the theory suggests that innovation will be a major element in the development of an artistic reputation.

Scale-free network theory also explains, or at least suggests, two qualities that are observable about cultural networks. One is that they are capable of enrolling people (nodes) across significant distances and maintaining a fair degree of internal consistency. To give an example, at any given time, it is usually fairly clear who are the current hot artists, hot opera singers and hot writers in a given culture—which can span continents. How do such ad hoc structures hang together? According to Mssrs. Barabasi and Bonabeau:

[Scale-free networks] can be amazingly resilient against accidental failures…[A]lthough hundreds of routers routinely malfunction on the Internet at any moment, the network rarely suffers major disruptions…Intuition tells us that the breakdown of a substantial number of nodes will result in a network’s inevitable fragmentation. This is certainly true for random networks: if a critical fraction of nodes is removed, these systems break into tiny, noncommunicating islands. Yet simulations of scale-free networks tell a different story…The random removal of nodes [from scale-free networks] will take out mainly the small ones because they are much more plentifyl than hubs. And the elimination of small nodes will not disrupt the network topology significantly, because they contain few links compared with the hubs, which connect to nearly everything.

However, another factor that is apparent in cultural networks is their susceptibility to sudden, often radical, shifts in taste. This seems to be a function of another aspect of scale-free networks: their susceptibility to an attack aimed at the hubs. As our authors explain:

In a series of simulations, we found that the removal of just a few key hubs from the Internet splintered the system into tiny groups of hopelessly isolated routers. Similarly, knockout experiments in yeast have shown that the removal of the more highly connected proteins has a significantly greater chance of killing the organism than does the deletion of other nodes [less highly connected proteins.] These hubs are crucial…

This shows that the most connected nodes—presumably, academics, record company executives, museum staffers, etc. in cultural networks—can, as long as they hold onto to their positions, maintain a viable system of consensus, even if suffering losses among the less connected nodes (i.e., people like you and me.) But when they are replaced, or retire, or whatever, the cultural network of which they are the hubs rapidly falls apart.

Lacking extensive documentation, these are of course merely conjectures, but if anyone goes to the trouble of proving all this, I’d appreciate sharing the Nobel Prize, okay?



P.S. Lynn Sislo at Reflections in d minor has taken up this point in an interesting posting entitled "Popularity." You can see this here.

posted by Friedrich at April 16, 2003


Admit it, you just want the Nobel so you can go check out the blonde Swedish power-hub thing.

Posted by: Yahmdallah on April 16, 2003 04:55 PM

I saw an article a few months ago that related this
to blogging, and by the miracle that is Google, I've
found it again: here it is.

Not surprisingly, the Professor is at the top of the power curve.

Posted by: Will Duquette on April 16, 2003 09:12 PM

Wow, great posting, and be sure not to miss the link Will passes along -- that's a fascinating peice too. Stockholm, here we come, provided I'm allowed to carry someone else's bags.

Posted by: Michael Blowhard on April 17, 2003 12:13 AM

Very stimulating, and leads on to further exploration.
For a similar observation about power nodes, see Elias Canetti's Crowds and Power, for which, among other works, I seem to recall he won the Nobel. Canetti, seeking to define the dynamic that moves crowds and mobs, postulated what he called "crowd crystals" – individuals radiating a kind of charisma or authority that created clusters around them. He also argued that action was triggered when these reached a certain critical mass. He observed that when these crowd crytals were removed, the activity of the crowd degenerated into c haos and it eventually was easily dispersed.

He also noted that police and others tasked with controlling crowds had some sort of basic instinct about how they worked. For example, he cited reports of how police often "stood by" as a mob sacked a building or set some hate object on fire. At this point its accumulated energy was sufficiently discharged for authorities to move in and take dispersive action without much opposition.

There is much more than this to Canetti's treatise, which was really seeking to divine the secret of leaders in manipulating masses of people. I feel I have seen Canetti's ideas given dramatic underpinning the last week or so in Baghdad.

This is tangential, perhaps, but I believe it is applying a similar principle to that related in Friedrich's summary, with roughly similar conclusions.

As to the web, could McCluhan ever have dreamt his global village would become first a city, then a world, then splinter into a billion villages again?

Posted by: Dave Farrell on April 17, 2003 07:15 AM

Thanks for the compliments, although it's clear from Will Duquette's link that other people are way ahead of me on this. Still, it would be interesting to do some kind of quantitative study of influence (either intellectual or financial) in the culture world and see if it, in fact, does follow a power law distribution. I would certainly be willing to place a modest bet that it would, simply because the cultureverse seems to operate very much as the theory predicts.

Oh, and Yamdallah, of course that's why I want the Nobel Prize. What's your point?

Posted by: Friedrich von Blowhard on April 17, 2003 11:21 AM

If you are interested in the hub/nodes and scale-free stuff, Barabasi's book, "Linked" is quite a good read.

Posted by: Bill Kaplan on April 21, 2003 05:03 PM

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