Circulated earlier from The Chronicle of Higher Education:

   "Judith Kleinfeld, the iconoclastic scholar best known for her
   controversial criticism of gender studies, has published a
   paper disputing the veracity of the research that led to the
   concept of 'six degrees of separation.'  The widely accepted
   theory that any two individuals are linked by an average of
   six acquaintances is based on the early work of the late
   Stanley Milgram..."

The 'degrees of separation' corresponds to the notion of DIAMETER in graph
theory: basically the longest out of all possible shortest paths between
pairs of people.

It is a standard result of mathematical graph theory (see "Random Graphs,"
Bela Bollobas, Cambridge University Press, pages 276 and 263) that
(rewording the theorem):

   For a sufficiently large randomly chosen network, with
   probability 100%, the diameter will be the small number d,
   which depends in a complex way on the size of the network
   and the average number of contacts per person.

This result of course assumes a uniformity of connections that does not take
geographical separation into account (although e-mail may have a greater
worldwide uniformity) but the diameter of the USA or worldwide social
networks cannot be much greater than the theorem predicts.  Exactly what the
diameter is is still an empirical question, but there can be no doubt that
for a sufficiently large social network the "small world phenomenon" holds.

The major difficulty is that people will not be aware of the shortest path
from them to some other person, although there is always a pleasant "Eureka"
feeling when you meet a stranger and discover the short path connecting you
to them...

Tony Dekker

-----
Dr Tony Dekker
DSTO C3 Research Centre, Fernhill Park
Department of Defence, Canberra ACT 2600 Australia

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