An evolution model for urban rail transit hyper networks based on allometric growth relationship

To address limitations of existing urban rail transit (URT) evolution models—including static selection mechanisms, inadequate adaptability across stages, and simplistic validation—this study proposes a dynamically optimized hypernetwork evolution model. By introducing a time decay factor γ, the model achieves a smooth transition from “scale-free preferential attachment” to “random connection” under the constraint of a fixed growth rate difference (GRD) between nodes. We construct a URT hyper network (stations as nodes, lines as hyper edges) and derive dynamic equations for node hyper degree and hyper edge hyper degree. Empirical validation using subway network data from Beijing, Shanghai, and Guangzhou (222–378 stations) was conducted via Python simulations, with model efficacy evaluated through Kolmogorov-Smirnov (K-S) tests and multi-index comparisons. Key findings include: Simulated topological features (e.g., degree distribution, hyper degree distribution) align closely with real networks (K-S test p > 0.05); Node hyper degree distribution evolves from power-law (early stage) to exponential (mature stage), consistent with empirical observations; The dynamic decay mechanism enhances adaptability (e.g., 15% increase in random connection probability per decade at γ = 0.1). This model provides a dynamic optimization tool for URT planning, particularly in hub layout design and network robustness enhancement.