X-Message-Number: 15191
From: "Mark Plus" <>
Subject: New York Times article on emergent Web
Date: Tue, 26 Dec 2000 08:11:56 -0800



December 26, 2000
First Cells, Then Species, Now the Web

As the Internet continues to proliferate, it has become natural to think of 
it biologically   as a flourishing ecosystem of computers or a sprawling 
brain of Pentium-powered neurons. However you mix and match metaphors, it is 
hard to escape the eerie feeling that an alien presence has fallen to earth, 
confronting scientists with something new to prod and understand.

The result has been an eruption of papers scrutinizing this artificial 
network and concluding, to many people's surprise, that it may be designed 
according to the same rules that nature uses to spin webs of its own. The 
networks of molecules in a cell, of species in an ecosystem, and of people 
in a social group may be woven on the same mathematical loom as the Internet 
and the World Wide Web.

"We are getting to understand the architecture of complexity," said Dr. 
Albert-Laszlo Barabasi, a physicist at the University of Notre Dame in 
Indiana whose research group has recently published papers comparing such 
seemingly diverse systems as the Internet and the metabolic networks of 
life-sustaining chemical reactions inside cells. The similarities between 
these and other complex systems are so striking, he said, "it's as if the 
same person would have designed them."

At the Polytechnic University of Catalonia in Barcelona, Dr. Ricard V. Sol  
and Jose M. Montoya, theoretical biologists in the Complex Systems Research 
Group, have recently found the same kind of patterns by studying computer 
models of three ecosystems: a freshwater lake, an estuary and a woods. 
"These results suggest that nature has some universal organizational 
principles that might finally allow us to formulate a general theory of 
complex systems," said Dr. Sol , who also works at the Santa Fe Institute in 
New Mexico.

In the past, scientists treated networks as though they were strung together 
at random, giving rise to a homogeneous web in which nodes tended to have 
roughly the same number of links. "Our work illustrates that in fact the 
real networks are far from being random," Dr. Barabasi said. "They display a 
high degree of order and universality that has been rather unexpected by any 

As they come together, many networks seem to organize themselves so that 
most nodes have very few links, and a tiny number of nodes, called hubs, 
have many links. The pattern can be described by what scientists call a 
power law. To calculate the probability that a node will have a certain 
number of links, you raise that number to some power, like 2 or 3, and then 
take the inverse.

Suppose, for example, that you have a network with 100,000 nodes that obeys 
a power law of 2. To find out how many nodes have three links, you raise 3 
to the second power, which is 9, and then take the inverse. Thus one-ninth 
of the nodes, or about 11,111, will be triple linked. How many will have 100 
links? Raise 100 to the second power, and take the inverse: one 
ten-thousandth of the 100,000 nodes   a total of 10   will be so richly 
connected. As the number of connections rises, the probability rapidly 

This kind of structure may help explain why networks ranging from 
metabolisms to ecosystems to the Internet are generally very stable and 
resilient, yet prone to occasional catastrophic collapse. Since most nodes 
(molecules, species, computer servers) are sparsely connected, little 
depends on them: a large fraction can be plucked away and the network will 
endure. But if just a few of the highly connected nodes are eliminated, the 
whole system could crash.

Not everyone believes that a universal law is at hand. A recent paper by 
Boston University physicists found deviations from the power-law pattern in 
a number of different networks, suggesting a more complicated story. But 
even so, the study found hidden orders that were far more interesting than 
the purely random patterns scientists have long used to analyze networks.

"The important point is that the networks are very different from our 
familiar model systems," said Dr. Mark Newman, a mathematician at the Santa 
Fe Institute. "This means that all our previous theories have to be thrown 

It has only been in recent years that computer power has grown enough to 
gather and analyze data on such intricate systems. In a highly publicized 
paper in 1998, Dr. Duncan Watts, a sociologist at Columbia University, and 
Dr. Steven Strogatz, an applied mathematician at Cornell University, found 
that many networks exhibited what they called the small-world phenomenon, 
popularized in John Guare's play "Six Degrees of Separation."

Just as any two people can be linked by a chain of no more than about six 
acquaintances, so can any node in a small-world network be reached from any 
other node with just a few hops. The two scientists found this hidden order 
in three networks that could hardly seem more different: the web of neurons 
forming the simple nervous system of the worm Caenorhabditis elegans, the 
web of power stations forming the electrical grid of the Western United 
States and (the finding that attracted the most attention) the web of actors 
who have appeared together in films.

The phenomenon has been popularized by a Web site, the Oracle of Bacon, at 
the University of Virginia's computer science department 
(www.cs.virginia.edu/oracle/) that calculates how closely an actor is linked 
to the film star Kevin Bacon. Patrick Stewart of Star Trek fame, for 
example, has a "Bacon number" of 2: he was in "The Prince of Egypt" with 
Steve Martin, who was in "Novocaine" with Kevin Bacon.

More recently Dr. Barabasi, working with a graduate student, Reka Albert, 
and a post-doctoral researcher, Dr. Hawoong Jeong, found that the World Wide 
Web is a small world   a phenomenon also noticed by two researchers at the 
Xerox Palo Alto Research Center in California, Dr. Bernardo A. Huberman and 
his student Lada A. Adamic. Any two documents or sites on the Web are 
separated by only a small number of mouse clicks.

The two teams also noted that the Web was structured according to a power 
law, with a handful of highly connected hubs and a steadily increasing 
number of less connected nodes   a fact noticed by other groups as well.

Reaching further, Dr. Barabasi and Ms. Albert found, in a paper last fall in 
Science, that a variety of networks may be organized this way. Included in 
their list were the small worlds of Dr. Watts and Dr. Strogatz as well as 
the connections on a computer chip and a network of citations in scientific 

The question is how this kind of order arises. In the same paper, the 
Barabasi group proposed a "rich get richer" effect: as new nodes are added 
to a network, they tend to form links with ones that are already well 
connected. New actors are more likely to be cast in films with well-known 
actors. New scientific papers are more likely to cite well-established ones. 
The result, according to their model, is a power-law distribution.

Their most recent sighting of the pattern was described in the Oct. 5 issue 
of Nature. Dr. Barabasi and his team worked with two members of the 
Northwestern University Medical School department of pathology to study the 
shape of metabolisms, the networks of chemical reactions inside living 
cells. Small molecules are linked to form large molecules, which are in turn 
broken back down into small molecules. But complex as these networks can be, 
they seem to obey a power law. In a paper recently submitted to the Journal 
of Theoretical Biology, Dr. Sol  and Dr. Montoya found a similar pattern in 
the ecosystems they studied.

The implication is that all these networks are extremely robust, shrugging 
off most disturbances, but vulnerable to a well-planned assault. "A random 
knockout of even a high fraction of nodes will not damage the network," Dr. 
Barabasi said. "But malicious attacks can."

Suggestive as the new theory is, other scientists are finding that the 
picture may not be so simple. In a paper published in October in the 
Proceedings of the National Academy of Sciences, Dr. Luis A. Nunes Amaral 
and his colleagues at Boston University analyzed a number of networks, 
including some of those studied by the Barabasi group. The list also 
included the hubs and spokes of the world airport system and two small 
friendship networks formed by a group of Mormons and by junior high school 
students. They concluded that while some networks obey power laws, in many 
others the pattern is distorted or nonexistent.

The deviations arise, the study proposed, because it is not always easy to 
add new nodes to a net: actors with more movie credits will attract more and 
more collaborators   until they get too old to act at all. Airports can only 
support so many new flights a day. Because of such complications, a network 
may fall somewhere on a spectrum between the extremes of randomness and 

Researchers are optimistic that they will sort out the details of a 
discipline that is still in its infancy. More important than any particular 
study, Dr. Watts said, is that scientists finally have the computer power to 
study real networks instead of just speculating about idealized ones.

"The real point is not to establish that everything is a power law," he 
said, "but to start modeling complex networks in a way that is informed by 
the data."

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