The diameter of the directed configuration model

preprint2020arXivOpen access

Abstract

We show that the diameter of the directed configuration model with nn vertices rescaled by log⁡n\log n converges in probability to a constant. Our assumptions are the convergence of the in- and out-degree of a uniform random vertex in distribution, first and second moment. Our result extends previous results on the diameter of the model and applies to many other random directed graphs.

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