Typical distances in ultrasmall random networks

Typical distances in ultrasmall random networks

Steffen Dereich, Christian Mönch, and Peter Mörters

Source: Adv. in Appl. Probab. Volume 44, Number 2 (2012), 583-601.

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.

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Primary Subjects: 05C80

Secondary Subjects: 60C05, 90B15

Keywords: Scale-free network; preferential attachment; configuration model; power-law graph; conditionally Poissonian graph; graph distance; diameter

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1339878725
Digital Object Identifier: doi:10.1239/aap/1339878725
Zentralblatt MATH identifier: 06055135
Mathematical Reviews number (MathSciNet): MR2977409

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