# The diameter of weighted random graphs

Leo Hamed Amini, Marc Lelarge

Research output: Contribution to journalArticle

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 language English (US) 1686-1727 42 Annals of Applied Probability 25 3 https://doi.org/10.1214/14-AAP1034 Published - Jun 1 2015 Yes

### 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 journalArticle

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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