Are Barabasi-Albert networks self-averaging?
  Yes and no. The size of the largest neighbourhood in a Barabasi-Albert scale-free entwork has string fluctuations of the order of the average value. The number of sites having exactly ten neighbours increases linearly in the network size while its relative fluctuations decrease towards zero if the number of sites in the network increases from 1000 to ten million. 
Dietrich Stauffer and Amnon Aharony