An Analytical Study of Hybrid Graph-Theoretic and Topological Models for Smart City Infrastructure Optimization

सार

The mathematical frameworks required to model complex and interdependent networks that have structural connectivity and resilience properties are needed for smart city infrastructure. This paper proposes a hybrid graph-topological model combining the graph theory and algebraic topology, which has been built to optimize urban infrastructure system. This study proposes new connectivity and resilience indices in this hybrid framework and provides theoretical optimization equation of network efficiency and fault tolerance. By leveraging general graph-theoretic concepts and topological analysis, we show that hybrid models can better represent complexity in multi-layered infrastructure than classical models. The research is based on three hypothesis statements, which are: Hybrid models offer better structural representation, newly developed indices improve the measurement of resilience and optimization equations increase efficiency. The results show the hybrid approach to identify the critical infrastructure vulnerabilities, quantify the redundancy patterns, and to perform predictive optimization across the three networks of transportation, water supply, and power. Theoretically, it provides the mathematical basis for future planning in smart cities; practically, it has implications for the resilience of infrastructure in fast-growing cities. Results suggest that topological persistence homology and graph algorithms can expose topological structure that is not visible using standard network analysis.

Keywords: hybrid graph-topological models, smart city infrastructure, network resilience, optimization algorithms, algebraic topology.