Mathematical Modeling of Resilient Infrastructure Networks in Smart Cities Using Hybrid Graph-Theoretic and Topological Methods

सार

Smart city infrastructure networks are prone to cascading failures which pose disruptions to service continuity and public safety. This study builds a hybrid graph-theoretic and topological model for adaptive and self-healing capabilities of interconnected infrastructure systems. Using symbolic mathematical modeling techniques that involved spectral graph analysis, persistent homology, and dynamic network topology, we were able to analyze the resilience mechanisms of a simulated urban water-power-transportation network of 347 nodes and 892 interdependent edges. Adjacency matrix spectral analysis, multi-layer network decomposition and topological data analysis with persistence landscapes were used as methodology. Results showed that hybrid models showed an average improvement of 34% in the recovery velocity and an average reduction of 28% in the cascade amplitude than traditional graph-based methods. Results from the hypothesis testing showed that topology-integrated frameworks had a significant influence on network stability (p < 0.001). The proposed general framework was extended to a wide spectrum of heterogeneous infrastructure systems, paving the way towards mathematical modeling of self-correcting urban systems. This work connects the disciplines of algebraic topology and network engineering, providing quantifiable measures of infrastructure resilience in smart cities and direct implications for the protection of critical infrastructure and the design of adaptive systems.

Keywords: resilient networks, graph theory, persistent homology, smart cities, cascading failures, topological data analysis, infrastructure modeling.