Detecting Critical Collapsed Nodes in Social Networks: A Cognitive Model of Resilience under Spatial Constraints

The resilience of social networks hinges on identifying users whose departure causes cascading collapse, influenced by both topology and social cognition, such as spatial relationship constraints. Existing studies often overlook how cognitive and behavioral factors shape network fragility. This paper introduces a cognitive-computational framework to detect critical collapsed nodes under spatial constraints, using the (k, σ)-core model to integrate social cohesion (k-core) and spatial thresholds (σ). We propose a pruning algorithm leveraging spatial locality for efficient querying of collapsed nodes and formalize the problem of finding optimal collapsed nodes as an NP-hard task. Our greedy heuristic prioritizes nodes with the most significant cascading impact, similar to human strategies in crises. Experiments on eight real-world networks show our model outperforms topology-only baselines in predicting collapse patterns, especially in spatially-embedded communities. Our findings highlight how spatial constraints and social cohesion amplify systemic fragility, providing insights for designing cognitively-aligned interventions to boost network resilience, bridging computational analysis with cognitive science.