Source: Adv. in Appl. Probab.
Volume 44, Number 2
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
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