The Diameter of Weighted Random Graphs

Details The Diameter of Weighted Random Graphs The Diameter of Weighted Random Graphs

2011-12-29

arxiv.org/abs/1112.6330v1

Mathematics

Probability

47 pages

Scientific paper

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 maximal weight of the shortest weight path between a random vertex and all others (the flooding time), as well as the (weighted) diameter of sparse random graphs, when the edge weights are i.i.d. exponential random variables.

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