Re: Position randomization

vive wrote:
> Try to see the network from the Kleinberg model as a platonian ideal form.
> We can try to replicate it by running the swapping algorithm, where nodes will
> prefer positions based on how they clustered in the original network, but the
> generated positioning will never (for all practical timescales) be more than a
> shadow of the perfect network. Hopefully it works rather well (surpringly well
> in simulation! :)) but still with its small faults and glitches in the
> assignments which affects the routing.

Two points: first, the Kleinberg model is probabilistic, so even an
ideal network generated according to the model will have glitches.
(Hence Oskar's simulations show a success rate less than 100% even
before the positions are randomised.) There are really no ideal
Kleinberg networks: there are only more-or-less Kleinbergish networks.

Second, you can use the Kleinberg model to attach a new node to any
network, even if it isn't a Kleinberg network: just attach the new node
to each existing node with a probability inversely proportional to the
distance. (Likewise you can use the Erdos-Renyi model to add a node to
any network even if it isn't an Erdos-Renyi network: attach the new node
to each existing node with equal probability, etc.)

>> Why would the connections between the other nodes make a difference?
> 
> Sorry, I didn't understand that.

Sorry, I meant why would you need to consider the existing connections
when connecting a new node? The connection probabilities are independent.

Cheers,
Michael