We show that in preferential attachment models with power-law exponent τ ∈ (2, 3) the distance between randomly chosen vertices in the giant component is asymptotically equal to (4 + o(1))log log N / (-log(τ - 2)), where N denotes the number of nodes. This is twice the value obtained for the configuration model with the same power-law exponent. The extra factor reveals the different structure of typical shortest paths in preferential attachment graphs.
"Typical distances in ultrasmall random networks." Adv. in Appl. Probab. 44 (2) 583 - 601, June 2012. https://doi.org/10.1239/aap/1339878725