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The Flooding Time in Random Graphs

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Abstract

Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class G p (N) of random graphs, the corresponding flooding time is investigated. The flooding time T N (p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time T N (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 p N satisfies Np N /(log N)3 → ∞ if N → ∞.

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Authors and Affiliations

  1. Information Technology and Systems, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Remco Van Der Hofstad, Gerard Hooghiemstra & Piet van Mieghem

Authors
  1. Remco Van Der Hofstad
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  2. Gerard Hooghiemstra
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  3. Piet van Mieghem
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Hofstad, R.V.D., Hooghiemstra, G. & Mieghem, P.v. The Flooding Time in Random Graphs. Extremes 5, 111–129 (2002). https://doi.org/10.1023/A:1022175620150

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  • DOI: https://doi.org/10.1023/A:1022175620150

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