The Annals of Applied Probability

The diameter of weighted random graphs

Hamed Amini and Marc Lelarge

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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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Ann. Appl. Probab., Volume 25, Number 3 (2015), 1686-1727.

First available in Project Euclid: 23 March 2015

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Zentralblatt MATH identifier

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

First-passage percolation weighted diameter random graphs


Amini, Hamed; Lelarge, Marc. The diameter of weighted random graphs. Ann. Appl. Probab. 25 (2015), no. 3, 1686--1727. doi:10.1214/14-AAP1034.

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