On Fri, 25 Jan 2002, Dekker, Tony wrote:
> 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.
Ah, but real world graphs are not random. See
for Albert-Laszlo Barabasi's work on the architecture of complex
networks, arguing strongly against the random graph approach of
Erdos. I'm just finishing up a read-through of a draft of his
forthcoming book and it's an excellent work that ties together a
lot of different views of complex network architecture into a
model that incorporates preferential growth. This leads to
network models that predict the presence of "hubs", nodes with a
high degree of connectedness, which are emphatically absent in
the random graph model.
Ann Arbor, MI
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