jhurley at infostations.com
Wed Nov 26 06:39:43 CST 2003
I have been reading the "Links, the new science of networks," by
One of the central theorems is that in random networks (randomly
placed links between nodes), all nodes will likely be linked if there
are *roughly* as many links as nodes. That is, starting from any
node, one can get to any other node by following links, provided
there are roughly equal numbers of nodes and links.
I would have guessed that many more would be required. (There are
many more links between neurons in the brain than there are neurons.)
This extraordinary theorem was derived by Paul Erdos (the most
prolific mathematician over the past 100 years) and Alfred Renyi.
I have no idea how to prove the theorem. (If anyone knows where I
could find this proof, I would appreciate the information.) It seems
so improbable. To satisfy myself I did the best I could; I went
looking for an experimental verification--enter Run Rev.
If you wish to experiment for yourself, run the following from the message box:
go url "http://home.infostations.net/jhurley/Networks.rev"
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