Fuzzy graphs in telecommunications: exploring average fuzzy cyclic connectivity for enhanced connectivity analysis

Fuzzy graph models occur specifically in the dynamic processes of physical, biological, and social systems. Data transmission reliability, routing optimization, and network failure detection are all aided by connectivity analysis of fuzzy graph models. The cyclic connectivity analysis in terms of cycles in fuzzy graphs has grown into a prominent field of study. As strong cycles between vertices serve as a critical path for information flow, we propose a connectivity metric that considers the significance of strong cycles, providing a comprehensive approach in the area of connectivity. In this paper we extends the average connectivity concepts in terms of the cycles in fuzzy graphs. Also, the average cyclic connectivity of subgraphs, complete fuzzy graphs, \(\theta \) $\theta$ -fuzzy graphs, and other related topics are examined. An algorithm for finding the new connectivity measure is provided and a practical implementation in real world scenarios is also discussed.