A novel approach for analyzing the structural integrity and operational vulnerability of complex networks using intuitionistic fuzzy graphs has been modeled. While traditional fuzzy graph metrics focus primarily on existence, they fail to capture the holistic systemic impact of failures. To overcome this limitation, a scalar-based measure of nodal importance that integrates both existence (membership degree) and non-existence (non-membership degree) values of incident edges into a single critical metric has been developed. The proposed indices demonstrate enhanced sensitivity to network perturbations compared to conventional degree centrality measures, capturing latent vulnerabilities in critical infrastructure topologies. Based on this, two indices are proposed: Intuitionistic Fuzzy Degree Index and Intuitionistic Edge Interaction Index. These indices quantify the total system activity, stress dispersion, overall network cohesiveness, and potential for cascading failure propagation. When applied to synthetic core-periphery networks, the proposed indices identified critical nodes with superior discrimination capability compared to existing fuzzy graph metrics, revealing that removal of identified nodes results in system-wide connectivity degradation observable through both membership and non-membership approximations. This methodology was applied to a core-periphery communication network to analyze the systemic consequences of node removal. Experimental validation on networks of varying sizes demonstrates that the Intuitionistic Edge Interaction Index achieves robust node criticality ranking across heterogeneous network topologies with improved predictive accuracy for cascade initiation points. This work provides network analysts and engineers a quantitative tool to precisely assess criticality and inform targeted resilience strategies in uncertain, high-risk environments.
Chandramohan et al. (Fri,) studied this question.