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 examples?

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 change.

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 society?”

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?

Let me focus only on the Internet, a complex network of computers connected by wires that allow them to communicate with each other. The most fascinating thing about the Internet is that it is not centrally designed. A network always evolves by the addition of new nodes. The nodes of the Internet are the routers—and there is no central blueprint telling us where can we one add a new one—any company can add its own router to the network without asking permission from anybody.  Therefore, the Internet took up all the characteristics of a self-organized network, becoming very similar to other complex networks in nature. It’s dominated by a few highly connected hubs that carry most of the traffic, and to which everybody connects. This is good news, as this self-organized structure makes the Internet resilient against unavoidable random local failures. But it carries its Achilles’ Heel, as a group of well-trained hackers could bring it down in no time.

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 Trade Center?

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.

You say that Vernon Jordan is only three handshakes away from any Fortune 1000 corporate director. Does that make him the country’s best networker?

It certainly makes him the country’s most central director. Jordan’s case is a wonderful example of the power of networks and networking: we can follow step-by-step how his first directorship, via network effects, has landed him on more and more company boards, eventually making him the most central director, with membership on eleven boards.  Once you follow his path and see how members of one board recommended him to members of other boards, you can understand why he emerged as a central node in the “six degrees of Monica Lewinsky” scandal.

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.