Image: Regular, Small World and Random Networks

Caption: As p increases from zero to one, the networks transition from regular to small world to random. The regular network has links at evenly spaced intervals while the small world network contain connections at evenly spaced intervals as well as some random connections as well. The random network has no mathematically calculated intervals and has only random connections.

Source: Duncan J. Watts, Columbia University
Credit: D. J. Watts and S. H. Strogatz, "Collective dynamics of 'small-world' networks" Nature 393, 441-443 (1998)
NSF funded: Yes (DMS-9500948, "Nonlinear dynamics of oscillator arrays," 7/1/95-6/30/98, and DMS-9627189 "Mutual synchronization of biological oscillators," 8/15/96-7/31/00)
NSF permission to use: YES (external and internal)

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