In your book, you say “we have taken apart the universe and have no idea
how to put it back together again.”
What do you mean by that?
Science is based on the
assumption that the devil is in the details. The jargon for this assumption is
reductionism. When trying to understand anything from the cell to the
ecosystem, we first seek to understand what it is made of, breaking it into
pieces. Understanding cancer has really been a quest to find the molecules that
cause it. Understanding the origins of the Universe was a race to reach down to
quarks and superstrings. To be sure, reductionism has been hugely successful.
We have drugs because we understood the molecular basis of some illnesses. We
have the Internet because we understood how the electrons move about in a
semiconductor. We always hoped, however, that once we understood the details,
it would be easy to reassemble the pieces, and understand the global behavior
of complex systems. Lately, scientists increasingly realize that this dream has
failed, because most systems are not simple.
They are made of so many and such diverse components that understanding
how they all work together is very difficult.
We are indeed in a situation of the crying child, who has taken apart
his favorite toy, but has no idea how to put it back together.
Why should we care about networks? You call them “the next scientific
revolution.” Are they really that big a deal?
Behind most complex systems
there is an intricate network. Life is encoded by a complex network of
molecules hidden within the cell. The Internet is a complex network of
computers connected by wires. The economy is a complex network of companies,
consumers, and regulatory agencies. Society is a complex network of people
connected by friendship, family, and professional ties. It has only been in the
past few years that we realized how important a role these networks play in
shaping the behavior of most complex systems. We learned that understanding
networks is the crucial prerequisite to comprehending complexity. Therefore,
many scientists from very different disciplines have started a frontal attack
to understand the webs with which nature surrounds us. One of the most
surprising findings is that most networks in nature are very similar to each
other. The social network is not that different from the four billion year old
chemical network within our cells or the decade old World Wide Web.
What are these similarities?
For several decades,
networks were believed to be fundamentally random, i.e. it was assumed that the
nodes, such as the pages of the World Wide Web, the people on the society, or
the chemicals of the cell, are randomly
wired together. Yet, as we started looking at real networks, we noticed some
reoccurring elements in all of them that increasingly undermine the random
hypothesis. On the World Wide Web my research group documented the existence of
a few websites, such as Yahoo.com, that have an extraordinary number of links
pointing to them. In society sociologists have noticed the existence of
connectors, a few individuals with an extraordinarily large number of
acquaintances. In the cell my group and others noticed the existence of a few
molecules that participate in just about all chemical reactions. These hubs, as
they came to be called, could simply not be explained using the random network
hypothesis. They were telling us that some common laws must exist, shared by
all networks, which are responsible for the hubs.
What role do these hubs play in networks? Can you give us some
If you inspect the flight
diagrams shown in glossy flight magazines, telling you which airports are
served by the airline, you will notice that most airports have only a few
links, while a few hubs are connected to just about all airports. Similar hubs
are present in most complex systems. A few hub molecules in the cell, or a few
highly connected individuals in society are the bridges of their respective
networks. These hubs have a dramatic impact on the behavior of all networks.
For example, on the Internet, hundreds of routers are broken in any
moment. Despite this, the Internet does
not crash—a robustness attributed to the hubs. Also, one of the reasons you do
not drop dead every time a molecule goes crazy in your body—and believe me,
there are millions of such misbehaving molecules—is that the network within the
cell is dominated by such hubs. On the other hand, if you know which are the
hubs, by taking them out you can easily destroy the whole system. Think of
simultaneously closing down the airports in Chicago, Dallas, New York, Detroit
and Denver—in hours all U.S. air travel would be halted. In the past few years
we learned that cells, the society, the Internet, and the economy all have
their O’Hare, offering them a high degree of robustness against random
failures, but making them fragile against attacks.
How do networks emerge, and how do they evolve?
Real networks always start
out with a few nodes, to which new nodes are added gradually. Think about the
World Wide Web: in 1991 it had only one webpage created by Tim Berners Lee.
Then people started adding more pages, connecting to each other. Node by node
the Web has grown to over a billion webpages. Life also emerged molecule by
molecule from a soup of chemicals about four billion years ago. The economy
grows company by company. These examples indicate that growth is a fundamental
property of all networks. But recently
we learned about another key element of network evolution: links are not placed
randomly either. You are more likely to know about Yahoo.com than my webpage,
and thus you link to it more often; companies are more likely to do business
with large, established corporations; you will more likely meet people that
have many friends. It turns out that most complex networks share two laws:
growth, and a subtle preference to link to the more connected nodes. In a
subtle way these two fundamental laws of network evolution are responsible for
the hubs, and many other topological features of real networks, ranging from
robustness to the spreading of computer viruses and fads.
What role do networks play in business?
A complex network describes
the organization of each company, the nodes being the employees and the links
the professional relationships between them. At the macroeconomic level there
is an another network, whose nodes are the various economic institutions, from
companies to government agencies, and the links represent the partnerships
between them. Recent studies indicate that these economic networks developed a
self-organized topology, very similar to the World Wide Web or the cell. The consequences of these findings are only
now being understood. In the last few years we learned that the 1977 Asian
economic crises, which took out companies and banks worldwide, could only be
explained if we incorporate the various network effects. The same is true for
the recent difficulties experienced by some of the leading companies of the
information revolution, such as Cisco or Compaq: they suffered straggling
losses by miscalculating network effects. It’s amazing how little attention has
been paid until recently to network effects in the economy. But there are signs that this is about to
What about the role of networks in society?
Society is the most familiar
network to all of us. We are the nodes, and the links are our social links. One
of the most popular features of social networks is known as “six degrees of
separation,” brought to the world’s attention by John Guare’s play by the same
name. The concept is based on Stanley
Milgram’s 1967 study indicating that people within the U.S. can be connected
via six handshakes. Our understanding of the social network is a bit
handicapped by the fact that we don’t have a map of it. But lately we have
rather reliable submaps. We have detailed maps of how scientists collaborate
with each other, and how actors work together in Hollywood. These maps captured the rise of Kevin Bacon
as a central figure in Hollywood. Such
a map is behind the Kevin Bacon game, which asks players to link actors to
Bacon based on movies in which they appeared together. These maps also allow us to assign a ranking
to all scientists based on the shortest path to Erdös via co-authorship. Most important,
however, these maps indicate that society is unable to avoid the universal laws
that govern the evolution of all networks around us: it’s dominated by hubs, a
direct consequence of its growing self-organized topology. A Martian visiting Earth, apart from the
scale, would not notice much of a difference between the social network, the
World Wide Web, or the web within our cells.
What do you mean when you say, “only one link is required to form a
Think about a group of
people at a party that don’t know each other initially. Then pick two and
introduce them to each other. Pick another two and introduce them as well. If
you continue doing such random introductions, you’ll see groups of people
emerging that will be connected to each other by social links. If you make only
a few introductions, islands of people will know each other, but have no
connections to other islands. The question is, how many introductions do you
need to make in order to guarantee that most people are part of a large cluster,
where you can reach from everybody to everybody else through a chain of
acquaintances? In the 1950s two mathematicians, Paul Erdös and Alfred Rényi,
offered the answer: when each person knows at least one other person in the
group, most people will be part of a large cluster. Highly counterintuitive, but one link is enough for the society
to emerge. This explains why nobody is isolated in the social network: we each
have far more than one acquaintance, guaranteeing that no one is left out of
the giant social cluster.
What role do networks play in technology?
Why haven’t hackers attempted to bring down the Internet yet?
If hackers take down the
Internet, they rob themselves of their favorite toy. Real hackers would never
do that. Rogue nations might, however. The reliance of the United States on the
Internet is overwhelming, which has lead to a very asymmetric threat: the U.S.
could gain little by breaking down the Iraqi Internet, but Iraq could create
significant destruction by disrupting the U.S. infrastructure. This is the
reason why many fear that as our dependence on the Internet deepens, terrorism
will move more and more toward cyber-warfare.
Does your network theory explain why the terrorists went for the World
It certainly gives us some
clues as to why this choice was the most appropriate from the terrorist’s
perspective. Most networks have an Achilles’ Heel: if you knock the hubs out,
you can inflict serious damage. The World Trade Center is probably the most
prominent single economic hub, the White House (which was supposed to be a
target) and the Pentagon are the most visible political and military hubs. But
network theory also helps us understand why the attacks failed to bring these
networks down: knocking out a single hub, even the biggest one, is never
sufficient. You have to go for the
whole hierarchy of hubs. Perhaps even more important, network theory helps us
understand how the terrorist networks emerged. It’s increasingly clear that
Osama bin Laden took advantage of the natural laws of network formation to
create his terrorist organization. The terrorist network’s non-centralized, hub
dominated structure offers a resilience not seen in regular armies, allowing it
to function successfully under very different conditions.
What would it take to knock “terrorist networks” down?
The answer is simple: knock
the hubs out. Yet, as I mentioned earlier, capturing the biggest hubs is not
sufficient. You really have to get the
whole hierarchy. But there are other ways as well: recent results indicate that
one can induce a natural self-destruction in a network by inducing a cascade of
internal failures. We have seen such cascading failures in the Asian financial
crisis and the 1996 California power failure. It was bad news for everybody
affected by it. We could turn such cascading failures to our advantage,
however, in the case of the terrorist networks.
What role do networks play in biology?
If there is any field where
understanding networks will bring an unmistakable revolution in the next
decade, biology is the one. We have the full list of the genes for humans and
dozens of simpler organisms. The most important lesson we learned from genome
mapping is how little we really know of how cells work. While we have a hint of
the components, we don’t know how these components interact, or how the
signatures of life emerge from the interactions of thousands of molecules.
Therefore, biology is on an incredibly fast track to map out the network behind
the cell, seen as the ultimate barrier for comprehending life. Just as I write
these lines, Nature and Science have published four major
studies telling us which proteins interact with which other proteins. A new
field has emerged, called bioinformatics, that aims to make sense of the
incredible amounts of network data collected by the experiments. The bulk of my current research is also in
this area. The advances taking place at
an unparalleled pace offer the potential for new drugs and a far better
understanding of what life is and how cells function.
Are you saying doctors will never cure cancer if they keep approaching
the disease on a gene-by-gene basis?
That is pretty clear to all
involved in cancer research. Most diseases, ranging from cancer to manic
depression, are not due to a single broken gene but arise from the interaction
of several malfunctioning genes and gene products. A good example is cancer.
The so-called p53 molecule is known to be mutated in a high percentage of
cancer patients. Yet, this molecule alone is not responsible for cancer. It
acts as a cellular cop—when mutated, it is unable to stop the harmful effect of
other gene disorders. Only when other,
cancer causing genes break down and interact with this p53 gene can we see
cancer developing. It’s increasingly clear, and frequently discussed in
scientific publications, that we won’t cure cancer until we fully understand
these network effects.
You claim it takes only six handshakes to get from person to person in
society. But you say it takes nineteen, on average, to get from website to
website. Does that mean word of mouth
is still more powerful than website buzz?
Perhaps the most important
aspect of this finding is not the difference between six and nineteen, but
their similarity. Look at it this way: six billion
people linked by six handshakes. Over
a billion webpages linked by nineteen clicks. I can continue the
list: close to a half million
Hollywood actors, each only three
links from other actors. Each molecule in the cell is only three reactions from the other molecules. A generic
property of networks is that they create small words: you can navigate between
a huge number of nodes with only a few links. It’s this universality of small
world behavior that I find intriguing. From this perspective there is little
difference between six and nineteen.
With regard to word of
mouth, the spread of buzz is less determined by the small world effect than by
the network’s topology. One of the most
incredible recent findings is that in hub-dominated networks, buzz and viruses
can spread indefinitely. This means
that no matter how weakly contagious a virus is, it has a fair chance to reach
all of us. This finding has turned
everything we know about how to protect ourselves from virus outbreaks upside
down, and explains why the weakly infectious AIDS virus has reached such a
significant percentage of the population.
Indeed, the sexual network is hub dominated—there are a few individuals
that have hundreds of sexual partners, and they have an incredible impact on
our ability to stop diseases.
What made you get interested in networks?
I lived in the Bronx at that
time, and visited Manhattan daily. One day I envisioned the millions of
Internet, phone, and electric cables hidden beneath the pavement that make the
city functional. You don’t see them, but you know that there’s a very complex
nervous system with uncountable nodes and links. I felt that there must be some
organizing principles that describe the structure of this amazing construct,
and I’ve been thinking about networks ever since. The project had a very long
incubation period, however: it was five years before this thinking resulted in
some tangible results when we predicted the diameter of the World Wide Web.
How has your knowledge of networks affected your personal life?
Well, since I started work on the book, I’ve
ceased to have a personal life…but seriously, it did give me a completely
different perspective on the world. Before many systems looked hopelessly
entangled and complicated. After uncovering the network behind them, they
became surprisingly simple and elegant. Phenomena that I was always baffled by,
from market crashes to cellular robustness, now make sense. In general, I have
a far better understanding of why and how things happen—from careers to
financial issues, from the rise of terrorism to searching the World Wide
Web—than I did before. I guess you could say this new approach changed the way
I internalize the events around me.