Graph-theoretic methods have seen wide use throughout the literature on multiagent control and optimization. When communication networks are intermittent and unpredictable, they have been modeled using random communication graphs. When graphs are time varying, it is common to assume that their unions are connected over time, yet, to the best of our knowledge, there are not any results that determine the number of finite-size random graphs needed to attain a connected union. Therefore, this article bounds the probability that individual random graphs are connected and bounds the same probability for connectedness of unions of random graphs. The random graph model used is a generalization of the classic Erdős–Rényi model, which allows some edges to never appear. Numerical results are presented to illustrate the analytical developments made.

中文翻译：

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随机图及其并集的非渐近连通性

图论方法在多代理控制和优化的整个文献中已得到广泛使用。当通信网络是间歇性且不可预测的时，已使用随机通信图对其进行了建模。当图随时间变化时，通常会假设它们的并集是随着时间而连接的，但是，据我们所知，没有任何结果可以确定实现连接并集所需的有限尺寸随机图的数量。因此，本文限制了各个随机图被连接的概率，并且为随机图的并集的连通性限制了相同的概率。所使用的随机图模型是经典Erdős–Rényi模型的概括，该模型允许某些边缘永远不会出现。数值结果表明了分析的发展。