The Flooding Time in Random Graphs

Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class Gp (N) of random graphs, the corresponding flooding time is investigated. The flooding time TN (p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time TN (p) converges in distribution to the two-fold convolution Λ(2*) of the Gumbel distribution function Λ (z)=exp (−e−z), when the link density pN satisfies NpN/(log N)3 → ∞ if N → ∞.