profrv at nex.net.au
Tue Apr 20 13:13:55 PDT 1999
Missed this link!
Nexus (Small World in Britain)
$25.95/£18.99 W. W. Norton/Weidenfeld & Nicolson
America's baseball superstar Yogi Berra has a sideline as a
man-in-the-street philosopher. His epigram, "It's déjà vu all over again",
sprang to mind while I was reading Linked and Nexus. Albert-Laszlo Barabasi
and Mark Buchanan deal with the emerging science of networks - how they
form, how information and matter move through them, how puzzling aspects of
everyday life can be explained by understanding their dynamics.
What's the message, then? Simply that all networks - -the Internet,
terrorist groups, multinational industries, interstate highways, Amazonian
ecosystems - follow the same simple and powerful rules. The "science of
networks" has sprung up to uncover these rules, and provide a firm
foundation for the care and feeding of these interconnected patterns.
Curious as to how Google came to be the most popular search engine on the
Internet or what it would take to dismantle the Al Qaida terrorist network?
The Barabasi volume will tell you. But if you want to understand the spread
of infectious disease, how riots form or why the rich always seem to get
richer, then Buchanan's treatment is for you.
The mathematician Paul Erdös published over 1500 papers with 507 co-authors
before his death in 1996. This prodigious output gave rise to something
mathematicians call the "Erdös number," an integer representing the number
of steps between Erdös and any given mathematician. Erdös obviously has
Erdös number 0. Anyone who wrote a paper with him has number 1. Anyone who
co-authored a paper with one of Erdös's co-authors has number 2, and so on.
A low Erdös number is a matter of considerable pride among mathematicians,
so important in fact that there is a Web page devoted to keeping track of
the Erdös number of thousands of mathematicians.
What is quite astonishing is that almost everyone - even a
non-mathematicians like Bill Gates - has a very low Erdös number, typically
between 2 and 5. This is a quintessential example of what Barabasi and
Buchanan call the "small worlds" phenomenon. Basically, this web of science
is a small world because it is a highly interconnected web, in which almost
all mathematicians are closely linked to each other via a short path of
The network of mathematicians and their Erdös numbers serves as a prototype
for just about every human social network - including the Internet, as both
Barabasi and Buchanan show. Suppose you look at a particular Web page and
ask how many clicks of your mouse it takes to get from this page to any
other page via hyperlinks. Barabasi and his students actually did this
calculation for their website at the University of Notre Dame. It contained
325,729 documents connected by 1,469,680 links. Counting up how many pages
had one link, two links, and so on, they discovered that the number of
pages having a certain number of links decreased by about a factor of five
each time the number of links was doubled.
These results lead to a simple relationship between the number of links in
a network and the number of nodes in the network having that many links.
Called a "power law", this relationship forms a central principle by which
networks structure themselves. As both authors point out, power laws play
as important a role in understanding networks as the famed bell curve of
the normal probability distribution plays in understanding the role in
statistics of independent random variables, such as a person's height.
Two other extremely important rules of networks are also considered in some
detail in each of these books. One of these is the "weak link" discovered
some 30 years ago by sociologist Mark Granovetter. It refers to the
seemingly paradoxical fact that the most important connections for
spreading information throughout a network are not the people who are most
closely connected to you. Rather, the key "connectors" are those who form a
bridge between the cluster of people you know and other, similar clusters
of close acquaintances of your friends. Thus, the links in a social network
are not established at random. Instead,they are strongly clustered, and
some of the connections are more important than others - that is, the ones
enabling one cluster to link to another.
These "busy bees" with an uncommonly large number of links to many clusters
are the people writer Malcolm Gladwell claims are responsible for creating
fashions and trends. They make deals happen and generally serve as agents
or middlemen who "tip" things in one direction instead of another. The
central idea of his book The Tipping Point (reviewed by Paul Marsden, 6
May, page 46) is that tiny and apparently insignificant changes can often
have consequences out of all proportion to themselves, accounting for the
transformation of unknown books into bestsellers or the rise of teenage
Both Buchanan and Barabasi give enlightening accounts of both Granovetter's
and Gladwell's work. Dig in, too, for fascinating accounts of the stability
of food webs, the formation of "old boys" networks, the "new economy", the
human genome, and much, much more.
Both books are extremely well-written, entertaining accounts aimed at the
intelligent lay audience. The overlap is inevitable: Barabasi and Buchanan
employ the same anecdotes, talk about the same people and use similar
diagrams to illustrate their message. Even the size and price of their two
books are roughly the same. You could call them two peas in a pod - but
their flavours are distinct. In short, both are to be heartily welcomed as
about the best introduction you could hope to get to the whys and
wherefores of networks, human and non-human.
John Casti is at the Technical University of Vienna
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