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ORIGINAL RESEARCH article

Front. Phys.

Sec. Statistical and Computational Physics

Volume 13 - 2025 | doi: 10.3389/fphy.2025.1596130

An Evolution Model for Urban Rail Transit Hyper Networks Based on Allometric Growth Relationship

Provisionally accepted
Zehua  ZhangZehua Zhang1ruining  weiruining wei1shumin  fengshumin feng1*lei  xvlei xv2Fan  YangFan Yang3hao  liuhao liu1yiqiang  jiangyiqiang jiang1
  • 1Harbin Institute of Technology, Harbin, China
  • 2Guangzhou Vocational College of Science and Technology, Guangzhou, China
  • 3Guangzhou Information Technology Vocational School, Guangzhou, China

The final, formatted version of the article will be published soon.

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.

Keywords: Urban rail transit, Hyper network, Allometric growth, Evolution model, Dynamic preferential attachment, K-S test

Received: 19 Mar 2025; Accepted: 16 Jun 2025.

Copyright: © 2025 Zhang, wei, feng, xv, Yang, liu and jiang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: shumin feng, Harbin Institute of Technology, Harbin, China

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