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Why Austrians Should Care About Network Science

December 22, 2003

Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life, by Alberto-Laszlo Barabási, The Penguin Group: New York, 294 pages.

I believe that Austrian economists can benefit from reading Linked, the recent book by Albert-László Barabási, a professor of physics at the University of Notre Dame. Barabási's ideas contain both promising paths and dangerous pitfalls for the Austrian paradigm.

The central thesis of Linked is Barabási's contention that, over the last forty or so years, a new science of networks has arisen. Its roots are in the branch of mathematics called graph theory. Contributions have been made to this emerging field by mathematicians, physicists, biochemists, business researchers, sociologists, and others.

Graph theory, first developed by the brilliant 18th-century mathematician Leonhard Euler, abstracts, from actual groups of things that are connected in some way, the idea of a web of links and nodes. The example that prompted Euler's interest in graph theory hopefully will illustrate just what the heck the previous sentence means.

In the 1700s the citizens of the city of Konisberg, Prussia, amused themselves by wondering whether there was any path that crossed over each of the city's seven bridges once and only once. By recasting the question as an abstract mathematical problem, in which each bridge was a node and each path between them was a link, Euler was able to prove that there was no such path. The idea of a node, which means any thing composing part of a network, and a link, which means any connection between those things, are the key concepts in the mathematical idea of a graph.

Graph theory made significant advances in the 1950s, through the work of mathematicians Paul Erdos and Alfred Renyi. Erdos was one of the most notable and admired mathematicians of the 20th century. He never held a steady job, academic or otherwise, and lived a nomadic existence, wandering from the home of one mathematician to another. He would arrive at a colleague's doorstep, declaring "my brain is open," and begin collaborating with his host. Erdos's unusual modus operandi produced over 1500 published papers, involving 507 coauthors.

Erdos and Renyi's model assumed that links in a network are randomly distributed between nodes. Although their work significantly advanced graph theory, subsequent research into real world networks gradually revealed the limits of their assumption.

One early example of the new wave of network thinking emerged in sociology. In 1967, Harvard professor Stanley Milgram performed a study in which he asked a random sample of people in Wichita, Kansas and Omaha, Nebraska, if they knew one of two people in Massachusetts. If they agreed to participate in the study but did not personally know the people in question, they were asked to forward the study folder to someone they thought was more likely to know the target person than they were. Milgram tallied the number of times the folder was forwarded before it reached someone who knew one of the targets, and who therefore returned the folder to him at Harvard.

Milgram's results suggested that the average number of social links needed to connect any two people in the United States was less than six. His findings entered popular culture when playwright John Guare made it the theme of a play, Six Degrees of Separation.

While contemplating Milgram's finding, I wondered how easily I could contact some person who seemed, at first, to be quite remotely connected to me. For instance, did I really know someone who knew someone… who knew George W. Bush, in six steps or fewer? It seemed doubtful, until it struck me that I could do it in three steps: Lew Rockwell, Congressman Ron Paul, George W. Bush.

The idea of an intricate network of social connectivity further penetrated popular culture with the popularity of the game "Six Degrees of Kevin Bacon," where one person would name an actor, whom the other players would try to link to Bacon using as few steps as possible. A valid link between two actors consisted in their having been in a movie together.

Barabási notes that the focus on Kevin Bacon as a connector for Hollywood actors was a result of historical circumstance. The three college students who first thought up "Six Degrees of Kevin Bacon" happened to be watching a movie he was in at the time. In fact, Bacon, according to a list compiled by a member of Barabási's team, is only the 876th most-connected actor in Hollywood. (The most connected turns out to be Rod Steiger.)

In one of the many charming anecdotes that Barabási sprinkles throughout his book, he notes that Paul Erdos, the mathematical genius and eminent network theorist mentioned above, is only four Hollywood degrees of separation from Kevin Bacon! Erdos played himself in N Is a Number, a movie documentary about his life. Another actor in the film can be connected to Bacon through three links, and so Erdos's "Bacon number" is four.

The research of Barabási's team on Hollywood connectivity and the structure of the World Wide Web yielded an important finding: neither Hollywood actors nor web sites are connected in the sort of egalitarian, random network assumed by Erdos and Renyi.

In many real world networks, some nodes have far more links than would be predicted if the number of links per node were randomly distributed, as in a bell curve. Barbasi calls such highly linked nodes in a network hubs. They are the crucial connectors that hold many networks together.

Far from being random, the distribution of links in many networks seems to follow a power law, which predicts many more extreme cases than does a bell curve distribution. Barabási explains a power law distribution as follows:

"If the heights of an imaginary planet's inhabitants followed a power law distribution, most creatures would be really short. But nobody would be surprised to see occasionally a hundred-feet-tall monster walking down the street. In fact, among six billion inhabitants there would be at least one over 8,000 feet tall."

As Barbasi's team and other researchers examined other existing networks, they found more examples where the network's integrity depended on important hubs, and where link distribution followed a power law. Among the examples Barbasi cites are the biochemical reactions that take place in living creatures, where certain key compounds act as hubs; modern market economies, where a number of hub-like businesses tie together many suppliers and consumers; and ecosystems, where certain organisms are far more connected in the food chain than the average creature.

All of Barabási's examples appear to be networks generated spontaneously by the independent interaction of the network's nodes, rather than networks that were planned from the top down. Emergent networks, despite their apparent dissimilarity, seem to display deep structural resemblances. If Barabási is correct in his surmise, then the study of such networks may yield significant insight into a variety of hitherto unconnected fields.

Barabási is an excellent writer of popular science, and Linked is a rewarding and lively read. His frequent excursions into the personalities of the people responsible for developing the science of networks spice up the more technical material quite nicely. Linked is a fine introduction to network theorizing for any layperson interested in keeping up with new developments in science.

However, I think that Barabási tries to extend his ideas too far in several instances. For example, he says that human languages are networks "held together" by synonyms, in much the same way that the World Wide Web is held together by key web sites having many links to and from other sites. But in exactly what sense do synonyms hold a language together? It is unclear to me, and Barabási does not offer any explanation.

Barabási also contends that computer viruses spread rapidly around the Internet due to the presence of key hubs in the network. But all of the evidence he presents for hubs on the Internet deals with Web servers or routers. Most computer viruses, on the other hand, spread via e-mail. The fact that Google.com is a highly linked site, and you visited it last week, has nothing whatsoever to do with the fact that your computer was infected with a virus yesterday because you opened an e-mail attachment that appeared to be from your friend. Perhaps the e-mail network also exhibits a structure with many key hubs, but Barabási never mentions this. As presented, his leap from the structure of the Web to the spread of viruses by e-mail is unjustified.

It would be silly for me to contend that only professional economists should comment upon economics: I am not a professional economist myself, and I'll spout off on the subject at the drop of a hat. However, Barabási commits a sin all too readily perpetrated by mathematicians, physicists, and engineers who dabble in economics: they simply apply a model from their own specialty to some area of the economy, without really grasping the topic in question. Barabási, for instance, first lists some networks in the economy: "There are policy networks, ownership networks, collaboration networks, organizational networks, network marketing..." He then contends, "It would be impossible to integrate these diverse interactions into a single all-encompassing web." Unfortunately, he does not seem to have noticed the price system of the market economy, which every day does exactly what he claims is impossible.

As I indicated at the beginning of this review, I believe Linked should be of special interest to Austrian economists. One problem faced by Austrians is that it has been difficult to formulate a "progressive research program," one which can engage a large number of economists, based on praxeological theory.

Mises claimed that only a handful of people alive in the world at one time are capable of fundamentally advancing praxeological economics. There is certainly a vast amount of historical material that Austrian economics can help to explain, but such work is a branch of history rather than being economics per se. So what, exactly, is an Austrian economist, who is perhaps very bright and capable, but is not one of the few who can advance basic theory, supposed to do with his time?

The work of people researching chaos theory, networks, and other studies of complex phenomena may provide an answer. The promise in the work of network theorists is that, if Austrians employ the tools those theorists have developed, it is quite possible that they might be able to build formal models reflecting key Austrian insights, such as the importance of entrepreneurs, the deep connections present throughout the price system, and the macroeconomic effects of government policies, such as artificially lowering the interest rate.

Creating and refining such models would provide a research agenda for the Austrian School. The models would demonstrate the mathematical consistency of Austrian ideas to those who only recognize mathematical demonstrations, as well as possibly providing predictive tools based on Austrian insights.

The notion that Austrians could be interested in creating mathematical models may strike some as contrary to the very spirit of the school. But I suggest that it need not be so, at least if the models are adopted with the proper caveats.

It is true that Austrian economists recognize that economic activity springs from purposeful human action. But many complex economic phenomena are the result "of human action but not of human design." Even something seemingly as simple as a price for a good emerges from the plans and actions of a multitude of individuals. It may be that not a single actor in a market entered it intending for the price to be what it turned out to be that day. The sellers probably hoped that the price would be higher, while the buyers hoped that it would be lower. It was the interaction of their individual efforts to achieve their individual goals that produced the actual price as an unintended outcome.

The idea that such unintended, emergent outcomes might be modeled successfully by the advanced mathematical theories dealing with complex phenomena, at least for a certain period of time, does not contradict any fundamental Austrian insights. We can agree with Mises that human action is fundamentally different than the mechanical processes described by the equations of physics or chemistry. And we can follow him in holding that there are "no constants in human action." But neither of those truths precludes the possibility of typical patterns emerging from the complex interactions of numerous individual purposes. And it is such patterns, rather than precisely deterministic equations, that are the subject of the cutting-edge research into the mathematics of complex systems.

The danger that I see, for an Austrian heading down this path, is that he may become so enamored of his models that he forgets about human action. Barabási so stumbles a few times. For instance, he calls the U.S. highway system an example of a "random network." By that he means, as far as I can tell, that the highway system is a network where the links between nodes are where they are due to pure chance.

While I have a dim view of the efficiency and perspicacity of the U.S. Federal Government, I am fairly certain that it did not flip coins or draw straws to determine where to place interstate highways. The highways are where they are due to purposeful decisions. It is interesting that the end result resembles a random network, but that doesn't mean that it is one.*

Despite these caveats, I believe that the potential benefits to Austrian economics from these new avenues of research are greater than the dangers. I suggest that Austrians investigate network science and consider how they might apply it in their own areas of interest.

* A potential research topic is whether centrally planned networks are more likely to resemble a random network than are those that emerge through the actions of individual decision makers who are the nodes of the network in question.

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Gene Callahan is the author of Economics for Real People. Send him  MAIL, and see his Mises.org  Daily Articles Archive.


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