In this paper we study first passage percolation on a random graph model, the configuration model. We first introduce the notions of weighted diameter, which is the maximum of the weighted lengths of all optimal paths between any two vertices in the graph, and the flooding time, which represents the time (weighted length) needed to reach all the vertices in the graph starting from a uniformly chosen vertex. Our result consists in describing the asymptotic behavior of the diameter and the flooding time, as the number of vertices n tends to infinity, in the case where the weight distribution G has an exponential tail behavior, and proving that this category of distributions is the largest possible for which the asymptotic behavior holds.

中文翻译：

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一般加权随机图中的泛洪和直径

在本文中，我们研究了随机图模型（配置模型）上的第一个通道渗透。我们首先引入加权直径的概念，它是图中任意两个顶点之间所有最优路径的加权长度的最大值，以及泛滥时间，它表示到达图中所有顶点所需的时间（加权长度）。图从一个统一选择的顶点开始。我们的结果包括描述直径和泛滥时间的渐近行为，作为顶点的数量n在权重分布的情况下趋于无穷大G具有指数尾行为，并证明此类分布是渐近行为成立的最大可能。