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.Comment: 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