As the system becomes more and more complex, we are usually in the state of indeterminacy. In the real world, the states of uncertainty and randomness are the two most common types of indeterminacy. An uncertain random graph is applied to describe a graph model with uncertainty and randomness simultaneously. This paper mainly focuses on the connectivity of two vertices in an uncertain random graph. Firstly, a local connectivity index is proposed to unveil the chance measure that two special vertices are connected in an uncertain random graph. Furthermore, a method for calculating the local connectivity index is formulated. In addition, some simplified forms of the method are developed, and an algorithm is designed to obtain the local connectivity index. Finally, the information relevant to the relationship between the local connectivity index and the connectivity index is discussed.

中文翻译：

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不确定随机图的局部连通性

随着系统变得越来越复杂，我们通常处于不确定状态。在现实世界中，不确定性和随机性状态是两种最常见的不确定性类型。应用不确定随机图来描述同时具有不确定性和随机性的图模型。本文主要研究不确定随机图中两个顶点的连通性。首先，提出了一个局部连通性指数来揭示不确定随机图中两个特殊顶点连接的机会度量。此外，还制定了计算局部连通性指数的方法。此外，还开发了该方法的一些简化形式，并设计了一种获取局部连通性指标的算法。最后，