The diameter of weighted random graphs
نویسندگان
چکیده
منابع مشابه
The Diameter of Weighted Random Graphs
In this paper, we study the impact of the introduction of edge weights on the typical distances in a random graph and, in particular, on its diameter. Our main result consists of a precise asymptotic expression for the (edge) diameter of sparse random graphs on n vertices (under some standard regularity conditions) when the edge weights are i.i.d. exponential random variables of rate one.
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Extending some recent theorems of Klee and Larman, we prove rather sharp results about the diameter of a random graph. Among others we show that if d = d(n) > 3 and m = m(n) satisfy (log n)/d 3 log log n -> oo, 2rf_Imd'/'nd+x log n -» oo and dd~2md~l/nd — log n -» -oo then almost every graph with n labelled vertices and m edges has diameter d. About twenty years ago Erdös [7], [8] used random g...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2015
ISSN: 1050-5164
DOI: 10.1214/14-aap1034