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# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Physics: the art of networking," by Philip Ball, *Nature Science Update,*25 October 2000.

Ball's article introduces the topic of "small world" networks with the conceptof the "small world of social networks" premise of the play *Six Degrees ofSeparation*. (This now-familiar idea is that everyone on the planet isconnected to any other randomly chosen person by a chain of no more than sixmutual acquaintances.) From there Ball summarizes: "In 1998 two researchers atCornell University found that `small-world' networks can be identified by aparticular mathematical relationship between the average shortest distancebetween two nodes and the total number of nodes." He distinguishes small-worldfrom random networks, identifying small-world networks as scale-free (such asthe World Wide Web). He also reports on recent research by Luis Amaral et althat identifies at least two other kinds of small-world networks which dependon the number of links a typical node has.

*--- Annette Emerson*