OT: Networks

[Jim Hurley]

I have been reading the "Links, the new science of networks," by 
Albert-Laszlo Barabasi.

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"

Jim