Optimizing connectivity in fuzzy graphs for resilient disaster response networks

Despite significant technological advances in recent years, communication challenges still persist. These issues are especially evident during crises, where system failures, network overloads, and incompatibilities among the communication technologies used by different organizations create major obstacles. Catastrophe scenarios are marked by high information uncertainty and limited control, which raises challenges for crisis communication. However, these aspects remain underexplored from a network-theoretic perspective. This study investigates the $(x,y)$-connectivity parameter between two nodes in a fuzzy graph, offering insights into network structure, robustness, and performance. We introduce a novel classification of nodes and edges into three categories: enhancing, eroded, and persisting, based on their impact on node-to-node connectivity. The behavior of these classifications is analyzed across different classes of fuzzy graphs. Furthermore, we establish upper and lower bounds for the $(x,y)$-connectivity under two graph operations. An efficient algorithm is proposed to identify and categorize nodes and edges accordingly. The practical relevance of our classification is illustrated through its application to disaster response communication networks, where maintaining resilient and adaptive communication is critical.