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