Network theory has a big role in driving fields like communication, e-commerce, and internet. There are several graph theoretical structures to represent natural and man-made networks. Stability and connectivity are two major factors associated with networks. A fuzzy graph is an effective representation for a weight normalized network. Different connectivity parameters in fuzzy graphs can be used to find stability and optimum flow in a network. In this article, we discuss cyclic connectivity, one of the major parameter that is closely related with cyclic reachability within a normalized network. Cyclic connectivity status and cyclic status sequence associated with a fuzzy graph are discussed. A classification of vertices of a network based on the cyclic connectivity status is given. Algorithms related to the topic along with their illustration are presented. Scope and significance of this parameter are presented with the help of real-life applications.

中文翻译：

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模糊图的循环连通状态


网络理论在推动通信、电子商务和互联网等领域发挥着重要作用。有几种图论结构来表示自然和人造网络。稳定性和连接性是与网络相关的两个主要因素。模糊图是权重归一化网络的有效表示。模糊图中的不同连接参数可用于找到网络中的稳定性和最佳流量。在本文中，我们讨论循环连接，这是与归一化网络中的循环可达性密切相关的主要参数之一。讨论了与模糊图相关的循环连接状态和循环状态序列。给出了基于循环连通状态的网络顶点分类。介绍了与该主题相关的算法及其插图。该参数的范围和意义通过实际应用来呈现。