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Spatial Topology and its Structural Analysis based on the Concept of Simplicial Complex

机译：基于简单复杂性概念的空间拓扑及其结构分析

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摘要

This paper introduces a model that identifies spatial relationships for structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer and a contextual layer. The identified spatial relationships are represented as a simplical complex, in which simplices and vertices, respectively, represent two layers of objects. The model relies on the simplical complex for structural representation and analysis. To quantify structural properties of individual primary objects (or equivalently simplices), and the simplicial complex as a whole, we define a set of centrality measures by considering multidimensional chains of connectivity, i.e. the number of contextual objects shared by a pair of primary objects. With the model, the interaction and relationships with a geographic system are modeled from both local and global perspectives. The structural properties and modeling capabilities are illustrated by a simple example and a case study applied to the structural analysis of an urban system.
机译：本文介绍了一种基于简单复杂性概念的结构分析识别空间关系的模型。通过重叠两个地图层（即主要层和上下文层）来识别空间关系。所标识的空间关系被表示为简单的复合体，其中，单纯形和顶点分别表示两层对象。该模型依赖于简单的复杂结构来表示和分析。为了量化单个主要对象（或等效的简单对象）以及整个简单复合体的结构特性，我们通过考虑多维连接性链（即一对主要对象共享的上下文对象的数量）来定义一组中心性度量。使用该模型，可以从本地和全局角度对与地理系统的交互和关系进行建模。通过一个简单的示例以及应用于城市系统结构分析的案例研究，说明了结构特性和建模功能。

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