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Flooding and diameter in general weighted random graphs

Part of: Combinatorial probability Graph theory Operations research and management science

Published online by Cambridge University Press:  04 September 2020

Thomas Mountford  and
Jacques Saliba Open the ORCID record for Jacques Saliba [Opens in a new window]
Thomas Mountford*
Affiliation:
Ecole Polytechnique Fédérale de Lausanne
Jacques Saliba*
Affiliation:
Ecole Polytechnique Fédérale de Lausanne
*
*Postal address: Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
*Postal address: Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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Abstract

In this paper we study first passage percolation on a random graph model, the configuration model. We first introduce the notions of weighted diameter, which is the maximum of the weighted lengths of all optimal paths between any two vertices in the graph, and the flooding time, which represents the time (weighted length) needed to reach all the vertices in the graph starting from a uniformly chosen vertex. Our result consists in describing the asymptotic behavior of the diameter and the flooding time, as the number of vertices n tends to infinity, in the case where the weight distribution G has an exponential tail behavior, and proving that this category of distributions is the largest possible for which the asymptotic behavior holds.

Keywords

First passage percolationconfiguration modeldiameterflooding timecontinuous branching process

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs 90B15: Network models, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 3 , September 2020 , pp. 956 - 980
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Copyright
© Applied Probability Trust 2020

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References

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