The diameter of weighted random graphs

Hamed Amini; Marc Lelarge

doi:10.1214/14-AAP1034

The diameter of weighted random graphs

Hamed Amini, Marc Lelarge

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper we study the impact of random exponential edge weights on the distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the maximal weight of the shortest weight paths between all vertices (the weighted diameter) of sparse random graphs, when the edge weights are i.i.d. exponential random variables.

Original language	English (US)
Pages (from-to)	1686-1727
Number of pages	42
Journal	Annals of Applied Probability
Volume	25
Issue number	3
DOIs	https://doi.org/10.1214/14-AAP1034
State	Published - Jun 1 2015
Externally published	Yes

Keywords

First-passage percolation
Random graphs
Weighted diameter

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/14-AAP1034

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abstract = "In this paper we study the impact of random exponential edge weights on the distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the maximal weight of the shortest weight paths between all vertices (the weighted diameter) of sparse random graphs, when the edge weights are i.i.d. exponential random variables.",

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AU - Lelarge, Marc

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N2 - In this paper we study the impact of random exponential edge weights on the distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the maximal weight of the shortest weight paths between all vertices (the weighted diameter) of sparse random graphs, when the edge weights are i.i.d. exponential random variables.

AB - In this paper we study the impact of random exponential edge weights on the distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the maximal weight of the shortest weight paths between all vertices (the weighted diameter) of sparse random graphs, when the edge weights are i.i.d. exponential random variables.

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The diameter of weighted random graphs

Abstract

Keywords

ASJC Scopus subject areas

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