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
