Replying to LO29976 --
Here's a review of the book I mentioned in the previous message.
Joe
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Albert-László Barabási, Linked, The New Science of Networks, Cambridge,
Massachusetts: Perseus Publishing, 2002
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Review by Joe Podolsky
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It was in high school, I think in a math class. The teacher said that almost
everything in the world could be explained by applying either a normal
(bell) curve or a power curve, one that follows the Pareto (80/20) Rule. I
haven't had much use for factoring polynomials, or whatever it was the class
was supposed to be about, but that bit of statistics has been the starting
point of just about any analysis I've ever done.
Every time I apply those rules, and every time they work, I'm always amazed.
I remember the first time I saw the huge quincunx in the Museum of Science
and Industry in Chicago. Thousands of ball bearings, dropped one by one,
banging randomly against pegs and always filling in a normal curve. What had
God wrought?
Albert-László Barabási, physics professor at the University of Notre Dame,
has written a book with an equal sense of awe. He wonders at two phenomena:
structures of networks and the frequency with which the nodes on networks
connect to each other. He starts off by joining the long line of
mathematicians, starting with Leonhard Euler in the late eighteenth century,
who believe that the understanding of graphs and networks is the key to
understanding what would otherwise appear as a random universe. Until only
about 40 years ago, mathematicians assumed that networks were, in fact,
random, with nodes distributed like a normal curve, dominated by averages.
This theory "predicts that most people have roughly the same number of
acquaintances; most neurons connect roughly to the same number of other
neurons; ...most Web sites are visited by roughly the same number of
visitors. As nature blindly throws the links around, in the long run, no
node is favored or singled out."
We now know that this is definitely not so. First came research in 1967 on
"degrees of separation" by experimental psychologist Stanley Milgram, who
showed that the median number of links between any two people in the United
States is only 5.5. More recently, experiments done by Barabási and some of
his graduate students showed that the 800 million nodes on the Worldwide Web
are, on average, only 19 clicks away from each other. The reason, first
noted in a 1973 paper by Mark Granovetter, is that networks have both strong
and weak ties. The strong ties form clusters, families, work colleagues,
church members, while the weak ties are the people who link the clusters
together, who are members of several clusters and who, therefore, pass
information around. Range is created through the weak ties. "Weak ties play
an important role in any number of social activities, from spreading rumors
to getting a job. ...To get new information, we have to activate our weak
ties." The strong ties merely reinforce what we already know.
Malcolm Gladwell popularized this notion in his 2000 book, The Tipping
Point. Gladwell asked approximately 400 college students to identify the
people they knew with a given surname, from a random list of surnames taken
from the Manhattan phonebook. The range was amazing, from two to 118. He
concluded that there " are a handful of people with a truly extraordinary
knack of making friends and acquaintances. They are connectors." Barabási
builds on this to make the point that's really obvious on the Web - that
publishing and visibility are not the same. The key is to be noticed, which
on the Web has to do with the number of sites that link to yours.
Which leads us back to the 80/20 rule, a distribution that mathematicians
call a "power law," yielding a "power curve" that is high on the left and
drops swiftly to a long, low tail on the right. Barabási says that "the
distinguishing feature of a power law is not only that there are many small
events, but that the numerous tiny events coexist with a few very large
ones." In a truly random network, the vast majority of the nodes have about
the same number of links, and the number of links form a bell-shaped curve.
The peak of the curve is called its characteristic "scale." Networks that
follow the power law, however, are not random and have no characteristic
scale; such networks are "scale-free." If we were to plot people's heights,
we'd get a normal curve, with a mean, median, mode and standard deviation
describing the scale. If we plot people's income, however, we'd get a power
curve. We'd find Bill Gates and Warren Buffett and the rest of the Forbes
400 with earnings far higher than those of everyone else in the world. No
characteristic scale describes that income curve.
The question is, what conditions have to be present for a scale-free network
to be formed? First is growth. The network has to be expanding; in fact,
there's a critical point at which the network transforms from the relative
order of a random network to the apparent chaos of a scale-free network.
Second, "the probability that a [node] will choose [to link] to a given node
is proportional to the number of links the chosen node [already] has." This
is called "preferential attachment." Better-linked nodes get more links and
therefore get still more links. As Barabási puts it, the rich get richer.
The nodes that are best linked become "hubs." These are the "mavens" that
Gladwell talks about in his book, the key people who know everybody and
influence everything.
First movers have an advantage in scale-free networks, because they have
less competition at first and can become better known and accumulate links.
But Barabási, still studying the Internet, wondered how latecomers can
overtake popular nodes. He wondered, for example, why Yahoo!, once the
obvious leader in search engines, was pushed aside by Google, an
underfunded, Johnny-come-lately.
The answer caused Barabási to add a third condition for scale-free networks:
competitive fitness. He realized that previous studies had assumed that all
nodes in a network had the same features and quality, except for the numbers
of links they had. In complex systems, however, each node has unique
characteristics. These characteristics vary among networks or even
communities with a network, but as long as other nodes in the network have
freedom of choice, they will choose to link to a node that is "more fit." An
observer can measure the rate at which a node is attracting more links. This
rate of attraction can be quantified as a measure of fitness. This
"fit-get-rich" behavior explains why latecomers can win.
One of the key issues in this post-9/11 world is the robustness and
vulnerability of networks. Simulations run on random networks and on
scale-free networks reveal an amazing fact: "There is a critical error
threshold below which [a random network] is relatively unharmed. Above that
threshold, however, the network simply falls apart. ...[But] computer
simulations we performed on networks generated by the scale-free model
indicated that a significant fraction of the nodes can be randomly removed
from any scale-free network without its breaking apart." This assumes that
failures affect both small and large hubs with the same probability. If,
however, in the worst case scenario, the few large hubs of a scale-free
network were specifically targeted, then the network would fail very
quickly.
Having built this base for the science of networks, Barabási illustrates the
impact of these ideas on a wide range of topics. He talks about computer
viruses and fads, the spreading of AIDS, and security on the Internet. He
describes studies that show that the Worldwide Web, because of the way that
sites are linked, is really a "directed" network, a network in which
messages flow just one way. As a result, Barabási shows that the Web can be
described as a "central core," "continents," "islands," and "tubes" linking
the pieces.
Perhaps the most interesting application of scale-free network science is
in, of all things (given that Barabási is a physicist), biology. Barabási
shows that the laws of growth, preferential attachment, and fitness can
explain the topology of cells and even some of the mysteries of natural
selection. He found that "cells are small worlds with three degrees of
separation. That is, most pairs of molecules can be linked by a path of
three reactions." He also found that, as with all scale-free networks, there
are organic molecules that are "most connected." In order, these are
adenosine triphosphate (ATP), adenosine diphosphate (ADP), and water. He
teases us with speculation about what this view of the biology might do for
understandings and treatments of diseases. Confidently, he predicts, "If
there is any area in which network thinking could trigger a revolution, I
believe that biology is it."
Because he sees networks in everything, Barabási next tackles the economy.
He talks about mergers and acquisitions and internal organizational
structures. He goes, however, far beyond the usual discussion of formal and
informal networks in a company. He talks about the alliances built inside
and outside the company, describing them as a scale-free topology that
follows the laws of growth, preferential attachment, and fitness. In a
discussion he could have taken from our daily newspapers, he points out that
the world of corporate directors is small, with only an average 4.6 degrees
of separation between any two board members of any company, based solely on
people who serve together on the same board, not including other possible
social or business connections. As with all scale-free networks, some
directors serve on many more boards than others do. Lawyer and political
consultant Vernon Jordan is the most connected, serving on 10 different
boards, meeting regularly with 106 other directors.
Barabási views the market economy as "nothing but a directed network" of
consumers, companies, financial institutions, and government agencies. He
applies weight to the financial size and frequency of transactions to infer
fitness.
At the very end, Barabási can not resist wrestling with the networks most on
our minds these days, terrorist networks. He sees Al Qaeda as a robust,
self-organizing, distributed network that has the benefits and weaknesses of
all scale-free topologies. We can't defeat it by destroying small hubs. We
can destroy this network only by finding and crippling the few large nodes
that have the most links in the network. But, as a fitting conclusion to the
book, Barabási recognizes that terrorists are networks of people, and
destroying their current set of links is not enough. "We must help eliminate
the need and desire of the nodes [the people] to form links to terrorist
organizations by offering them a chance to belong to more constructive and
meaningful webs. No matter how good we become at winning each net battle, if
we are unable to inhibit the desire for links [for destructive purposes],
the [terrorist] net war will never end."
This is an ambitious book. Barabási sees networks in everything. Perhaps he
is reaching too far when he sees networking as an all-purpose analytical
tool. But at the very least, he's given us a useful tool, another way of
looking at the world. And he's helped me understand why the comment about
bell curves and power curves is the one thing that has stuck with me from
that math class.
> -----Original Message-----
> > On the possibility you haven't come across the book
> already, I thought I
> > might share with you a quick summary/interpretation/taste
> of "The Tipping
> > Point: How Little Things Can Make a Big Difference," by
> Malcolm Gladwell
> > (2000): http://www.gladwell.com/ .
>
> While I enjoyed "The Tipping Point", considering Gladwell was
> describing
> non-linear social systems that had significant feed back and
> delay, I was
> surprised not to find any reference to either Systems Dynamics or Jay
> Forrester.
--"PODOLSKY,JOE (HP-Cupertino,ex1)" <joe_podolsky@hp.com>
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