曲面网络
Surfacic networks
AI总结：
本文提出用于分析二维流形上曲面网络的工具（懒惰路径、图艰辛度、额外努力），发现高程波动显著影响介数中心性且额外努力呈非普适幂律分布，为表面环境复杂系统建模提供新框架。
摘要：
曲面网络是构建在二维流形上的结构。许多系统，包括交通网络和各种城市网络，都属于这一类别。节点高程的波动意味着与典型平面网络存在显著偏差，需要专门的工具来理解其影响。在此，我们提出了这些工具，包括最小化高程差异的懒惰路径、衡量最短路径疲劳程度的图艰辛度，以及表征最短路径上正高程变化的额外努力。我们使用曲面网络的玩具模型来展示这些度量，并实证研究了选定城市中的行人网络。具体而言，我们考察了高程变化如何影响介数中心性的空间分布。我们还证明了额外努力遵循非平凡幂律分布，其指数并非普适的，这表明无论起点与终点之间的高程差异如何，沿最短路径遇到陡坡的概率都显著。这些发现凸显了高程波动在塑造网络特征中的重要性。曲面网络为全面分析和建模位于或受限于表面环境的复杂系统提供了一个有前景的框架。
英文摘要：
Surfacic networks are structures built upon a two-dimensional manifold. Many systems, including transportation networks and various urban networks, fall into this category. The fluctuations of node elevations imply significant deviations from typical plane networks and require specific tools to understand their impact. Here, we present such tools, including lazy paths that minimize elevation differences, graph arduousness which measures the tiring nature of shortest paths, and the excess effort, which characterizes positive elevation variations along shortest paths. We illustrate these measures using toy models of surfacic networks and empirically examine pedestrian networks in selected cities. Specifically, we examine how changes in elevation affect the spatial distribution of betweenness centrality. We also demonstrate that the excess effort follows a non-trivial power law distribution, with an exponent that is not universal, which illustrates that there is a significant probability of encountering steep slopes along shortest paths, regardless of the elevation difference between the starting point and the destination. These findings highlight the significance of elevation fluctuations in shaping network characteristics. Surfacic networks offer a promising framework for comprehensively analyzing and modeling complex systems that are situated on or constrained to a surface environment.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
