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 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.
Citation
Steffen Dereich. Christian Mönch. Peter Mörters. "Typical distances in ultrasmall random networks." Adv. in Appl. Probab. 44 (2) 583 - 601, June 2012. https://doi.org/10.1239/aap/1339878725
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