This is awesome, thank you, #[1]. Interesting that the mean is at N=3, max deviation is at N=5 but I am guessing the probability distribution of a social network distribution is determined by the follows, relays and connection between each follows/relays in order to find the community structure? I am not a mathematician so perhaps you and other mathematicians here would know this better. Question for #[2], did Twitter practice a degree of separation on the network that we know worked? (minus the algo)