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"Graph Theory in Practice: Part II," by Brian Hayes. American Scientist, March/April 2000, pages 104-109.
This continuation of Hayes's article in the January/February 2000 issue of American Scientistresumes his exploration of mathematical graphs, which are networks of nodes connected by edges. The article discusses the peculiarities of "small-world" graphs, which are named, as Hayes explains, "after the familiar cocktail-party experience of making a new acquaintance in a distant city and discovering you have a friend in common." The article describes the work of mathematicians Duncan Watts and Stephen Strogatz, who figured out a way of interpolating between graphs with edges placed in a completely uniform fashion, and graphs with edges placed in a completely random fashion. Their methods provide new ways of analyzing small-world graphs.
--- Allyn Jackson
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