Abstract

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 logN/ (-log(τ − 2)), whereNdenotes 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.

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