Inhomogeneous spatial networks - beyond the weak decay regime

非均匀空间网络 - 超出弱衰变范围

• 批准号: 443916008
• 负责人: Dr. Christian Mönch
• 金额: --
• 依托单位: Arbeitsgruppe Stochastik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/443916008?language=en
• 关键词: Inhomogeneous; spatial; networks; beyond; weak

Complex Networks arise throughout the sciences wherever large systems of interacting objects are investigated. In this project we study a rich class of mathematical network models that satisfy three basic principles: scale-freeness, the small-world property and clustering. To generate the models we form graphs consisting of randomly distributed vertices equipped with a weight, which are then connected by edges. The generation of each edge takes into account both the spatial distance between its endvertices as well as their weight. Our goal is to understand the behavior of these models by answering questions such as: When are there large connected components? What are their topological properties, e.g. connectivity and interpoint graph distances? Do they qualitatively behave more like lattices or more like trees? And what happens if we randomly remove edges from them?

复杂的网络出现在整个科学领域，无论研究的是相互作用的物体的大系统。在这个项目中，我们研究了一类丰富的数学网络模型，它们满足三个基本原则：无标度、小世界性质和聚类。为了生成模型，我们形成由随机分布的带有权重的顶点组成的图，然后这些顶点通过边连接起来。每条边的生成既考虑了其端点之间的空间距离，也考虑了它们的权重。我们的目标是通过回答以下问题来理解这些模型的行为：何时存在大型连接组件？它们的拓扑性质是什么，例如连通性和点间图距离？它们在性质上更像格子还是更像树？如果我们随机移除边会发生什么呢？