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June 2015 The diameter of weighted random graphs
Hamed Amini, Marc Lelarge
Ann. Appl. Probab. 25(3): 1686-1727 (June 2015). DOI: 10.1214/14-AAP1034

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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Hamed Amini. Marc Lelarge. "The diameter of weighted random graphs." Ann. Appl. Probab. 25 (3) 1686 - 1727, June 2015. https://doi.org/10.1214/14-AAP1034

Information

Published: June 2015
First available in Project Euclid: 23 March 2015

zbMATH: 1351.60009
MathSciNet: MR3325285
Digital Object Identifier: 10.1214/14-AAP1034

Subjects:
Primary: 05C80, 60C05
Secondary: 90B15

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 3 • June 2015
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