The diameter of weighted random graphs

Leo Hamed Amini, Marc Lelarge

Research output: Contribution to journal › Article

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1686-1727
Number of pages42
JournalAnnals of Applied Probability
Volume25
Issue number3
DOIs
StatePublished - Jun 1 2015
Externally publishedYes

Fingerprint

Weighted Graph
Random Graphs
Precise Asymptotics
Sparse Graphs
Random variable
Path
Random graphs

Keywords

  • First-passage percolation
  • Random graphs
  • Weighted diameter

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

The diameter of weighted random graphs. / Amini, Leo Hamed; Lelarge, Marc.

In: Annals of Applied Probability, Vol. 25, No. 3, 01.06.2015, p. 1686-1727.

Research output: Contribution to journal › Article

Amini, LH & Lelarge, M 2015, 'The diameter of weighted random graphs', Annals of Applied Probability, vol. 25, no. 3, pp. 1686-1727. https://doi.org/10.1214/14-AAP1034
Amini LH, Lelarge M. The diameter of weighted random graphs. Annals of Applied Probability. 2015 Jun 1;25(3):1686-1727. https://doi.org/10.1214/14-AAP1034
Amini, Leo Hamed ; Lelarge, Marc. / The diameter of weighted random graphs. In: Annals of Applied Probability. 2015 ; Vol. 25, No. 3. pp. 1686-1727.
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