Oskar Sandberg wrote:
To put actual numbers to this, I did simulations of point to point
routes using the same algorithm that I think is being used in Dijjer
(the one described in my thesis, with 20 shortcuts, but without using
"local" links):
<>
256000 12.572815
512000 15.743066
I let this simulation run further, and here are the results the next
results:
Run size: 1024000
(474 of 10000 successful: 0.0474)
(Mean Steps: 471.88397)
This means that the network with 20 links undergoes a phase transition
between 500 thousand and one million nodes, after which it doesn't work
at all (this behavior isn't surprising). So if the network should grow
to over half a million nodes, you definitely need more than 20 edges
(and caching won't help).
// oskar
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