### Abstract

Original language | English |
---|---|

Pages (from-to) | 583-601 |

Journal | Advances in Applied Probability |

Volume | 44 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2012 |

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*Advances in Applied Probability*,

*44*(2), 583-601. https://doi.org/10.1239/aap/1339878725

**Typical distances in ultrasmall random networks.** / Dereich, Steffen; Mönch, Christian; Morters, Peter.

Research output: Contribution to journal › Article

*Advances in Applied Probability*, vol. 44, no. 2, pp. 583-601. https://doi.org/10.1239/aap/1339878725

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TY - JOUR

T1 - Typical distances in ultrasmall random networks

AU - Dereich, Steffen

AU - Mönch, Christian

AU - Morters, Peter

PY - 2012/6

Y1 - 2012/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84872078657&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1239/aap/1339878725

U2 - 10.1239/aap/1339878725

DO - 10.1239/aap/1339878725

M3 - Article

VL - 44

SP - 583

EP - 601

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 2

ER -