Hamed Amini, Marc Lelarge
Published 2011-12-29, updated 2015-04-16Version 2
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.
Comments: Published at http://dx.doi.org/10.1214/14-AAP1034 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Applied Probability 2015, Vol. 25, No. 3, 1686-1727
Shortest-weight paths in random regular graphs
Finding minimum spanning trees via local improvements
Flooding in Weighted Random Graphs
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