Centrality-Driven Minimal Hamiltonian Loops to Boost the Resilience of Spatially Embedded Networks

The resilience of spatially embedded infrastructure networks—their capacity to withstand disruptions and recover functionality—has become increasingly critical in an era of escalating environmental and anthropogenic threats. While existing research emphasizes topological robustness, few strategies address both structural and functional resilience through geometrically constrained design. We present a novel framework that enhances network resilience via centrality-optimized minimal Hamiltonian loops (MHLs). Our approach integrates: (1) multi-metric node identification using neighborhood-augmented degree, eigenvector, closeness, and betweenness centrality; (2) genetic algorithm optimization (crossover=0.8, mutation=0.5) for MHL construction under spatial constraints; and (3) attack-recovery simulations across theoretical networks and four major subway systems (Beijing, Shanghai, London, New York). Empirical results demonstrate consistent resilience gains, but the effectiveness varies systematically with network topology: The Minimal Hamiltonian Loop (MHL) strategy based on betweenness centrality dominates in hierarchical systems such as the Beijing subway system, whether under single-node attacks or multi-node attacks. In contrast, the strategy based on degree centrality performs better in the New York subway system, which is similar to a scale-free network. This metric-adaptive framework provides a paradigm shift in infrastructure design, showing how loop geometries can be engineered to balance redundancy and resource efficiency. Our findings establish MHLs as a potent tool for next-generation resilient infrastructure, with direct applications to urban transit, power grids, and emergency response systems.