Simplicial analysis and community detection in cognitive modelling of complex systems

An integrated framework for the analysis of complex systems is presented through the application of simplicial complexes and community modularity. Cognitive maps of under-ground tunnel systems are employed as a case study, where Q-analysis is combined with community detection to reveal latent structures and connectivity patterns. Higher-order interactions are captured by constructing primal and dual simplicial complexes, followed by the assessment of q-connectivity and eccentricities. Community detection is performed using the Louvain method, enabling the evaluation of modularity without predefined assumptions. The results indicate that the analyzed tunnel-system map exhibits poor overall connectivity, with several vertices identified as structurally redundant in terms of system controllability. Nevertheless, the community detection procedure reveals a strongly modular structure, with six distinct functional domains encompassing technical infrastructure, risk management, technological systems, environmental impacts, economic recovery, and traffic dynamics. These findings highlight the utility of simplicial and modularity analyses for uncovering vulnerabilities and organizational regularities in critical infrastructure systems. The proposed framework provides decision-makers with a formalized toolset for improving governance, risk assessment, and strategic planning in contexts where multidimensional interdependencies play a defining role.