LBERT-LASZLO BARABASI, a professor of physics at the University of Notre Dame, became fascinated with the structure of the Internet in 1998. He and his student researchers designed software robots that went out on the Net and mapped as many of its nodes, hubs and links as they could. He then began studying other networks and found that they had similar structures. The Internet in particular, he found, had taken on characteristics of a living ecosystem.

That made for a valuable insight in itself. But Professor Barabasi went a step further and analyzed the genetic networks of various living organisms, finding that their genes and proteins interacted in much the same networked way as the Internet.

This conclusion, described in Professor Barabasi's new book, "Linked: The New Science of Networks" (Perseus Publishing, $26), could alter the way we think about all the networks that affect our lives. Those networks may be Hollywood power brokers, Vernon E. Jordan Jr.'s corporate board directorships or Al Qaeda terrorists. The Apostle Paul had a network of cities to spread Christianity.

Professor Barabasi's well written book will be understandable to most readers, but its core concept takes a moment to absorb.

Start by thinking of a highway map of the United States before the advent of the Interstate System. Each city, or node, was connected pretty much at random to others in the network of American cities. Each city has the same relative weight, or "scale," in Professor Barabasi's terminology. Knocking out one city doesn't disrupt the network. Traffic can be rerouted easily.

In contrast, consider the airport hub-and-spoke system that dominates the nation's airline transportation. A few nodes like Chicago, Atlanta and Dallas-Fort Worth have become far more important than, say, Lincoln, Neb. Knocking out the important nodes has serious cascading effects throughout the network.

This is similar to a disruption on the Internet. Because the nodes of these networks do not have the same scale, Professor Barabasi calls them scale-free, a concept that permeates the book.

Once you understand that concept, you're off on an intellectual detective journey. Professor Barabasi has invented a vocabulary to talk about the structure of networks.

"We are witnessing a revolution in the making as scientists from all different disciplines discover that complexity has a strict architecture," he writes. These networks do not operate at random, the author contends; there are laws that govern their behavior.

In the case of human genes, scientists have decoded the genes and proteins of DNA, but that is just the first important step in understanding how genes and proteins interact, Professor Barabasi says. The next step, he writes, is understanding how genes and proteins interact as part of a network, and he predicts the discovery of a clear set of rules for their behavior that will help unlock some mysteries of the human body.

Professor Barabasi makes that prediction partly because he and his researchers mapped out the interactions of 43 primitive organisms and found they took the form of a network with rules.

There are many examples of scale-free networks. Even a cocktail party can be mapped that way: the most sociable people are the "hubs" that link all the guests in a pattern that can be drawn. Other scale-free networks include the electrical power grid, companies and consumers linked by trade and the nervous system of living creatures.

 
Business writers have long talked about "network effects," meaning that a network generates more power than individual parts can do by themselves. That was part of the intellectual case against allowing Microsoft to dominate so many personal computers using its operating system.

But Professor Barabasi has put more flesh on the relatively primitive concept of the network effect. His work is relevant not only to physicists and mathematicians, but also to business executives, computer scientists, sociologists and biologists.

Networks have strengths and weaknesses, and Professor Barabasi contends that we have to understand both. On the positive side, because of the multiplicity of connections, some things happen quickly. A good idea can win rapid acceptance.

Professor Barabasi uses the example of Hotmail's explosion in popularity. Created on July 4, 1996, by Sabeer Bhatia and Jack Smith, it had one million users within a year. By the time Microsoft came knocking on the door to buy it a year later, it had 10 million. "Innovations and products with a higher spreading rate have a higher chance of reaching a large fraction of the network," he argues.

By contrast, networks have what he describes as an Achilles' heel. Knocking out a single major hub can cripple the network, which the Sept. 11 attacks almost succeeded in doing. In the United States, the airline system, financial markets and telecommunications networks all suffered grievous blows.

The extensions of Professor Barabasi's thinking go in many directions. What caused Cisco Systems and other technology companies that outsource much of their production to be so clobbered in 2000 and 2001? Cisco, in particular, had bragged that its Internet-based supply chain meant that it would never be surprised by having too much inventory. But, Professor Barabasi writes, Cisco did not understand network effects and had to pay for billions of dollars' worth of components in its extended supply chain; oddly, Cisco, the master of the network, didn't think in network terms.

"A me attitude, where the company's immediate financial balance is the only factor, limits network thinking," Professor Barabasi says. "Not understanding how the actions of one node affect other nodes easily cripples whole segments of the network."

Professor Barabasi makes a provocative argument about "the market." For hundreds of years, economists like Adam Smith have argued that there may be an "invisible hand" guiding the market but at the end of the day people cannot understand how the market works because it is too big, too complex, too random.

Nonsense, Professor Barabasi says. "In reality, the market is nothing but a directed network," he writes. "Companies, firms, corporations, financial institutions, governments, and all potential economic players are the nodes."

If you understand the structure and evolution of this network, you can, in fact, understand how the market performs, the author contends. That is sure to bring howls of derision from proponents of the dismal science known as economics.

If there is any criticism that can be leveled at him, it is that the reader is left wanting to understand more of the implications of his work. If we understand the network of the human body, can we cure cancer? If we understand the network of the global economy, can we stop recessions? If we understand the network of Al Qaeda, can we eradicate terrorism? The answers may be elusive, but Professor Barabasi's argument suggests that answers may indeed be found.