Science News Online (8/22/98): References for Close Connections

References & Sources - August 22, 1998

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Close Connections

It's a small world of crickets, nerve cells, computers, and people

Minor changes in the arrangement of links between members of a network can dramatically alter the rate at which information, computer viruses, or infectious diseases spread throughout the system.

References:

Watts, D.J., and S.H. Strogatz. 1998. Collective dynamics of 'small-world' networks. Nature 393(June 4):442.

Further Readings:

Bollobás, B., and F.R.K. Chung. 1988. The diameter of a cycle plus a random matching. SIAM Journal on Discrete Mathematics 1:328.

Chung, F.R.K. 1997. Spectral Graph Theory. Providence, R.I.: American Mathematical Society.

Collins, James J., and Carson C. Chow. It's a small world. Nature 393(June 4):409.

Peterson, I. 1998. The Jungles of Randomness: A Mathematical Safari. New York: Wiley.

______. 1996. Groups, graphs, and Paul Erdos. Science News Online (June 15).

______. 1996. Keeping the beat. Science News 149(April 13):236.

______. 1991. Step in time. Science News 140(Aug. 31):136.

A description of an enormous graph describing mathematical collaborations can be found at http://www.acs.oakland.edu/~grossman/Erdoshp.html.

You can play the Kevin Bacon game (involving connections between movie actors) at http://www.cs.virginia.edu/~bct7m/bacon.html.

Sources:

Carson C. Chow
Department of Mathematics
Boston University
Boston, MA 02215

Fan R.K. Chung
Department of Mathematics
University of Pennsylvania
Philadelphia, PA 19104-6395
Web site: http://www.math.upenn.edu/~chung

James J. Collins
Department of Biomedical Engineering
Boston University
Boston, MA 02215

Simon A. Levin
Princeton Environmental Institute
Princeton University
Princeton, NJ 08544-1003

Steven H. Strogatz
Department of Theoretical and Applied Mechanics
212 Kimball Hall
Cornell University
Ithaca, NY 14853
Web site: http://www.tam.cornell.edu/Strogatz.html.

Duncan Watts
Lazarsfeld Center for the Social Sciences
Columbia University
812 International Affairs Building
420 W. 118th Street
New York, NY 10027

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