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Connect, They Say, Only Connect

January 25, 2003

The whiteboard in Duncan J. Watts's office at Columbia
University was a thicket of squiggly blue lines, circles
and calculus equations. Mr. Watts, an associate professor
of sociology, had just begun a passionate disquisition on
the virtues and liabilities of scale-free networks when the
telephone rang. It was Alfred Berkeley, the vice chairman
of Nasdaq, hoping to chat about the exchange's design.

Mr. Watts, 31, is a network theorist. And these days that
means fielding frequent calls from powerful admirers like
Mr. Berkeley - Wall Street moguls and government officials
eager to tap into a nascent academic science that few
understand but that many think may hold the key to
everything from predicting fashion trends to preventing
terrorism, stock market meltdowns and the spread of HIV.

Never mind that Mr. Watts's new book on the subject, "Six
Degrees: The Science of a Connected Age," which will be
published by W. W. Norton next month, is littered with the
arcana of theoretical physics as well as charts and graphs
that appear to require an advanced degree in math in order
to decipher. Network theory is hot. Two other recent books
on networks, "Linked: The New Science of Networks"
(Perseus, 2002) by Albert-Laszlo Barabasi and "Nexus: Small
Worlds and the Groundbreaking Science of Networks" (W. W.
Norton) by Mark Buchanan, have already sold tens of
thousands of copies.

And that's not counting sales in the burgeoning genre of
consumer studies, where network science terms and concepts
are invoked with near religious fervor. From Malcolm
Gladwell's three-year-old best seller, "The Tipping Point,"
to just-published analyses like "The Influentials" and
"Branded: The Buying and Selling of Teenagers," the shelves
at Barnes & Noble are laden with books alternately
applauding and deploring the importance of things like
hubs, connectors, mavens and influencer teens for creating
fads, cementing brand loyalty and swelling profits.

"Network theory has become a bit of a fad," Mr. Watts
conceded after hanging up the phone. "I spend half my time
telling people I think it's relevant to a lot of problems
people care about and half my time trying to tone down the

Network scientists study networks: collections of people or
objects connected to each other in some way. Think of the
1.5 million Manhattan residents or the 30,000 genes inside
a human cell. Such networks, scientists argue, behave in
ways that can't be understood solely in terms of their
component parts. Without knowing what every single person
or object within the network is doing, they say, it's
nevertheless possible to know something about how the
network as a whole behaves.

Stated that way it sounds simple. But as an intellectual
approach, network theory is the latest symptom of a
fundamental shift in scientific thinking, away from a focus
on individual components - particles and subparticles - and
toward a novel conception of the group. As Mr. Barabasi, a
professor of physics at the University of Notre Dame, put
it: "In biology, we've had great success stories - the
human genome, the mouse genome. But what is not talked
about is that we have the pieces but don't have a clue as
to how the system works. Increasingly, we think the answer
is in networks."

Not that network theory is an entirely contemporary
creation. Its roots stretch back nearly 300 years, to
Leonhard Euler, a brilliant 18th-century Swiss
mathematician who dabbled in nearly every branch of modern
science, from algebra to astrophysics. In 1736, Euler took
up a brain teaser that had preoccupied the residents of
Königsberg, a Prussian town on the Pregel River not far
from where he lived: how to cross all seven bridges in town
without crossing the same bridge twice. No one had been
able to pull off the feat, but Euler provided the
mathematical proof that it could not be done. To do so, he
turned the problem into a network, depicting the bridges as
lines and the landmasses they connected as nodes.

After Euler, mathematicians continued to analyze networks,
then called graphs, enumerating the properties of orderly
and static structures like ice crystals and beehives. No
one thought to tackle networks of people or objects that
were, as Mr. Watts puts it in his book, "actually doing
something - generating power, sending data or even making
decisions." Such complex real-world networks were assumed
to be random: nodes and links connected in an arbitrary,
disorderly fashion.

But clearly this is not always the case. "Imagine that you
really did pick your friends at random from the global
population of over six billion," Mr. Watts writes. "You
would be much more likely to be friends with someone on
another continent than someone from your hometown,
workplace or school. Even in a world of global travel and
electronic communications, this is an absurd notion."

Of course, studying a network of six billion people is an
unfathomable proposition. It wasn't until the mid-1990's
and the advent of powerful computers that network
scientists were able to analyze real-life networks of
significant size and complexity. And in doing so, Mr. Watts
and his colleagues made some tantalizing discoveries. By
1998, they had found that networks as diverse as actors,
power grids, the World Wide Web, the proteins in a human
cell and the neurons of a wormlike organism called C.
elegans aren't random at all but obey the same simple,
powerful rules.

For example, whether the network has nearly a billion nodes
(the estimated number of Web pages) or just half a million
(roughly the number of actors in the Internet Movie
Database), the paths between any two nodes tend to be
extremely short - such that, for example, any two movie
actors can be connected by an average of less than four

That may not seem like news to anyone who has played the
Kevin Bacon Game - in which film actors invariably turn out
to have starred in a movie with Mr. Bacon or else with
another actor who has - or seen John Guare's play "Six
Degrees of Separation." (The play was inspired by the
famous 1967 experiment in which the Harvard social
psychologist Stanley Milgram tried to prove that anyone in
America could reach anyone else through a chain of fewer
than six people.) But it was not entirely clear why these
should all be "small-world" networks. As Mr. Watts points
out, "There is nothing similar at all about the detailed
way in which movie actors choose projects and engineers
build transmission lines."

Eerier still, in 1999, Mr. Barabasi and a student at Notre
Dame found that many of these small-world networks are also
what scientists call scale-free. Many natural phenomena,
including traits like height and I.Q., tend to cluster
around an average (producing the familiar bell curve
distribution). By contrast, scale-free networks go in for
extremes: a few hubs - nodes with lots of links - and many
more nodes with hardly any links at all. (Think of Google,
the search engine, as a hub, and your personal homepage -
which probably has just a few links - as an ordinary node.)

Mr. Barabasi's discovery startled scientists. "People
always knew there were networks but thought they were
random," he said. "To know they were nodes linked by hubs
was very unexpected."

It also provoked a frenzy of research. For as Mr. Barabasi
and his collaborator were able to show, the structure of
scale-free networks has important practical implications.
If you remove a few nodes at random, the network can still
function normally. But if you remove one of the hubs, the
results can be catastrophic.

Inspired by this insight, cancer researchers are now homing
in on the cell's hub proteins in order to learn how to
defend them from devastating attacks. Epidemiologists
studying sexually transmitted diseases are arguing that it
makes more sense to identify and treat the hubs in the
transmission network than to give drugs to everyone. "The
Bush administration's policy to give drugs to mothers with
children is completely irrelevant to stopping AIDS in
Africa," Mr. Barabasi said. "It's much better to go and
target the hubs."

Even the United States military has begun recruiting
network theorists to conduct counterterrorism research,
with the goal of learning how to protect information and
economic networks at home and destabilize terrorist
networks abroad.

Yet just which network model describes human society
remains a subject of fierce debate. Mr. Barabasi believes
the human social network is scale-free with the expected
smattering of richly connected hubs. Mr. Watts disagrees.
"If you asked people to list the number of people they
recognize, that could be scale-free, everyone recognizes
Michael Jordan," he said. "But if you said, `Who would you
trust to look after your kids?' That's not scale-free. As
you start to ratchet up the requirements for what it means
to know someone, connections diminish."

Is society a small-world network of the sort Milgram was
interested in? Mr. Watts spent the past year trying to test
that idea, using the Internet as a proxy for the world
population. Whatever the results, he says, it's clear that
human psychology has not yet adapted to the implications of
a connected world.

"We like to think of our world as full of atomized
individuals," he said. "But decisions people make and the
actions they take are so hopelessly entwined with the
behaviors of everyone else that it's difficult to draw the
boundaries around the individual." When it comes to
choosing a CD or explaining the success of Harry Potter,
your preference may matter less than the network's.

But some scholars dismiss the network hypothesis
altogether. Judith S. Kleinfeld, a psychologist at the
University of Alaska at Fairbanks, prompted a flurry of
media attention last year when she published an article
questioning the validity of Milgram's small-world findings.
Given the prevalence of networks - from power grids to
airports to the Internet - it's tempting to assume that
human society is a network as well, she says. But
ultimately, that is impossible to prove.

"Duncan assumes the world is a matrix," Ms. Kleinfeld said
in a telephone interview. "He wants to know how you get
from one point on it to another. But what if the world
isn't a matrix? What if people aren't all connected? What
if they're islands in space?"

Mr. Watts admits that he faces daunting empirical
challenges - and that overzealous scientists are a concern.
"You can turn almost anything into a network," he said,
holding up two papers he had received on the "small world
of human language" and shaking his head. "So what?"

"When I'm brutally honest with myself, I think that if we
can figure this out, we can answer some important
questions. Other times, I think it's just too hard."

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