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

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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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

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1244.05199
MathSciNet: MR2977409
Digital Object Identifier: 10.1239/aap/1339878725

Subjects:
Primary: 05C80
Secondary: 60C05, 90B15

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 2 • June 2012
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