从线路到网络,从线路到网络
1Centre d'Analyse et de Mathématique Sociales (CNRS/EHESS), Institut de Physique Théorique, Université Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France and , 54 Avenue de Raspail, 75006 Paris, France.
Physical review. E
|January 21, 2026
概括
本研究介绍了空间网络的新型基于线的增长模型,揭示了通用核心和分支架构. 该模型准确地预测了在地铁和真菌网络等现实世界系统中观察到的网络扩展行为.
科学领域:
- 复杂系统科学 复杂系统科学
- 网络理论 网络理论
- 数学建模的数学建模
背景情况:
- 大多数空间网络模型都侧重于基于节点的增长.
- 现实世界的网络往往通过线路的延伸和交叉增长 (例如地铁系统,真菌菌).
- 在理解由空间扩展组件构成的网络方面存在差距.
研究的目的:
- 介绍基于线增长和交叉的空间网络形成的最小模型.
- 研究这些直线成长网络的新兴架构和扩展行为.
- 为复杂系统提供超越基于节点的方法的通用范式.
主要方法:
- 开发了一个模型,在该模型中,线条以贪的方式生长,以最大限度地提高当地覆盖率,交叉现有结构.
- 将角连续性和几何约束纳入线增长过程中.
- 分析了新兴网络架构 (核心和分支) 和扩展特性.
主要成果:
- 基于线的增长模型自发地产生了一个核心和分支架构.
- 观察到非微不足道的缩放行为,包括次方程交叉增长.
- 确定了与经验数据一致的新出现的弗洛里指数和碎形维度.
- 空间缩放指数与点分布异质性相关,匹配地铁系统数据.
结论:
- 提出的基于线的增长模型捕捉了各种现实世界网络的关键组织特征.
- 展示了扩展元素的增长如何塑造大规模网络架构.
- 建立了理解空间网络超越节点中心模型的通用范式.
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