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From: Barry Wellman <wellman@CHASS.UTORONTO.CA>
Subject: power laws again
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***** To join INSNA, visit http://www.insna.org *****
UC Davis News & Info
Why the Rich Get Richer
April 2, 2007
graphic: concentric circles with colored bars
Networks like this show how some points can get many more
connections. (Raissa D'Souza/UC Davis graphic)
A new theory shows how wealth, in different forms, can stick to some but
not to others. The findings have implications ranging from the design of
the Internet to economics.
Real-world data -- whether distributions of wealth, size of earthquakes or
number of connections on a computer network -- often follow power-law
distributions rather than the familiar bell-shaped curve. In a power-law
distribution, large events are reasonably common compared to smaller
events.
Networks often show power laws. They can be caused by the "rich get
richer" effect, also known as "preferential attachment," where nodes gain
new connections in proportion to how many they already have. That means
some nodes end up with many more connections than others. The phenomenon
is well known, but had been assumed to be just a fundamental property of
networks.
Raissa D'Souza, an assistant professor at the Department of Mechanical and
Aeronautical Engineering and the Center for Computational Science and
Engineering at UC Davis, together with colleagues at Microsoft Research in
Redmond, Wash., UCLA and Cornell University, looked at how "preferential
attachment" can arise in networks.
"'The rich get richer' makes sense for wealth, but why would it happen for
Internet routers?" she said.
D'Souza and colleagues found that they could make tradeoffs between the
network distance between nodes and the number of connections between them.
By tweaking the conditions, they could make preferential attachment -- a
power-law distribution of the number of connections -- stronger or weaker.
These tradeoffs in networks are an underlying principle behind
preferential attachment, D'Souza said. The general framework could be
extended to all kinds of different networks, in biology, engineering,
computer science or social sciences.
"It's exciting because it shows the origins of something that we had
assumed as axiomatic," D'Souza said.
The other authors on the study, which is published online in the journal
Proceedings of the National Academy of Sciences, are Christian Borgs and
Jennifer T. Chayes at Microsoft Research, Noam Berger at UCLA and Robert
D. Keinberg at Cornell University. A figure from the study will also be
used for the cover art of the April 10 print issue of the journal.
Barry Wellman
_____________________________________________________________________
Barry Wellman S.D. Clark Professor of Sociology NetLab Director
Centre for Urban & Community Studies University of Toronto
455 Spadina Avenue Toronto Canada M5S 2G8 fax:+1-416-978-7162
wellman at chass.utoronto.ca http://www.chass.utoronto.ca/~wellman
for fun: http://chass.utoronto.ca/oldnew/cybertimes.php
_____________________________________________________________________
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-- Dragomir R. Radev Associate Professor SI, CSE, Ling U. Michigan, Ann Arbor http://www.eecs.umich.edu/~radev radev@umich.edu
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