In this age of the Internet, it seems that we're starting to think of practically everything in terms of networks. There are telephone networks and electrical networks, of course. There are the world's financial networks that move trillions of dollars each day. Microsoft's dominance in computer software is described as proof of the "Network Effect." Biologists use phrases like "protein network" to describe the way that proteins within a cell communicate with one another. We network at parties, trying to hook up with people who are more important than we are. And what discussion of networks would be complete without the Al Qaeda terrorist network? Networks have become the stuff of our nightmares.
It's tempting to think these networks are all so different that the term "network" has become meaningless. In fact, the reverse may be true. In "Linked," physicist Albert-László Barabási shows how all of these networks (and many more) follow the same basic mathematical rules rules that Barabási and his students at Notre Dame are largely responsible for discovering.
"Linked" is Barabási's first popular book, and it gets off to bit of a rocky start. Barabási's discoveries over the past five years have been revolutionary, but that's only because there was an orthodoxy to revolt against.
To make this clear, "Linked" spends the first four chapters discussing the graph theory of the 18th-century mathematician Leonhard Euler and the random network theory of 20th-century mathematicians Paul Erdos and Alfréd Rényi. This could get tedious fast, but the math is surrounded with a lively narrative. By the end of the fourth chapter, most readers will understand the mathematical foundations that have been used to analyze networks for the past 50 years. There is just one problem with this math: It's probably wrong.
The world, argues Barabási, is not random. People who want to sell their junk on the Internet click to eBay; there are dozens of websites to buy books, but most people click to Amazon. While trying to map out the links on the World Wide Web, Barabási and a student discovered the mathematics behind what many people seem to know instinctively: Some sites on the Web are immensely more popular than others. These sites Barabási calls "hubs."
We are all familiar with hubs. They're the points on a network that are responsible for the mass movement of money, ideas, and materials. For example, the network of Hollywood might have nodes that represent each actor, with lines drawn to connect the actors who have worked together in the same movie. The more popular nodes are called hubs; in Hollywood, these are the popular actors who get all of the good roles.
But what makes them a hub isn't the fact that they have a lot of connectors it's the fact that when new nodes are added to the network, these new nodes preferentially attach to hubs, rather than to a random node.
The real contribution of this network theory is not that it describes how networks are arranged, but that it describes how networks grow. By modeling this growth, the basic theory can describe emergent network properties in hundreds of different kinds of networks. Quite an accomplishment, considering that the concept of what are called "scale-free" networks is less than five years old.
Barabási weaves "Linked" together with a narrative that's part travelogue, part gossip column. He paints a picture of academia in which mathematics has truly become a social science, with some of the best work being done at conferences in idyllic European villages. Reading "Linked" makes one feel like a trusted student who gets to hear all the teacher's good stories. By the middle of the book, it's clear that the world of mathematics is its own network.
Indeed, it's Barabási's ability to bring all of these different networks together in one short volume that makes "Linked" such a pleasure to read. And it's the fact that all of these networks can be explained and understood using the same concepts, and the same mathematics, that makes this book so important.
Simson Garfinkel is the author of 'Database Nation: The Death of Privacy in the 21st Century' (O'Reilly).