Advances in Applied Probability

Typical distances in ultrasmall random networks

Steffen Dereich, Christian Mönch, and Peter Mörters

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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.

Article information

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

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1339878725

Digital Object Identifier
doi:10.1239/aap/1339878725

Mathematical Reviews number (MathSciNet)
MR2977409

Zentralblatt MATH identifier
1244.05199

Subjects
Primary: 05C80: Random graphs [See also 60B20]
Secondary: 60C05: Combinatorial probability 90B15: Network models, stochastic

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

Citation

Dereich, Steffen; Mönch, Christian; Mörters, Peter. Typical distances in ultrasmall random networks. Adv. in Appl. Probab. 44 (2012), no. 2, 583--601. doi:10.1239/aap/1339878725. https://projecteuclid.org/euclid.aap/1339878725


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