We show that the diameter of the directed configuration model with $n$ vertices rescaled by $\log n$ 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.

中文翻译：

---

定向配置模型的直径

我们表明，带有 $n$ 顶点的定向配置模型的直径由 $\log n$ 重新缩放，其概率收敛到一个常数。我们的假设是分布中均匀随机顶点的入度和出度的收敛，一阶和二阶矩。我们的结果扩展了先前关于模型直径的结果，并适用于许多其他随机有向图。