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.
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"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).
