The Representation, Measure And Analyses Of Spatial Network Graph

Geospatial network is not only the essential groundwork people depend on, but also the indispensable skeleton of the geo-space in which the whole society exist. The spatial network graph is the mathematical form of the real geospatial network. As a highly abstract form of spatial network phenomena, the spatial network graph discards some detailed geographic characteristics. The focus of the spatial network graph is the mathematical description of spatial network and the methods used in spatial network cognition are always mathematical. As a matter of fact, the abstraction from the spatial network to the spatial network graph is a cognitive means of the geography environment, which is also a leap from perceptual knowledge to rational knowledge. In the abstraction process, the essence is revealed. The main work of this dissertation is summarized as follows.1. Based on the analysis of the spatial network graph research, the concept of the spatial network graph is proposed and the relation between the spatial network and the spatial network graph is illustrated. From the current status quo of the representation, measure and analyses of the spatial network graph, the author determines the aim, scope and guidelines of the dissertation.2. Besides the basic characteristics of common spatial information, the spatial network has its unique properties, which are characterized by linearity, topology and connexity. The concepts and features with respect to the spatial network graph are described mathematically. Meanwhile, the difference between the spatial network graph and the mathematical network graph is analyzed, and illustrations on the spatial network graph elements as well as their attributes are made. As a result, a formalized description of the spatial network graph is proposed. And the spatial distribution types as well as structural characteristics of the spatial network graph within geographic space are summed up.3. Analysis is made on the algebraic expression, matrix expression and the character of the spectrum and eigenvalue as well as applications of the spatial network graph. The commonly used matrix transformation methods are discussed and the invariants in matrix transformations are explained.4. The index system of the measure of the spatial network graph is established, in which the fractal dimensions as well as their geographic meaning of the spatial network graph based on the fractal theory are discussed in detail, and the important indices for the connexity and stability of the spatial network graph are illustrated. The emphasis is put on the methods of computation and evaluation of the connexity and reliability of the spatial network graph, their actual geographic meanings and applications. Optimization and improvement are made due to the complexity of current methods.5. The cognitive models and methods are summed up, and the aspects that the spatial network data model should embody are put forward. The spatial network based 3-level abstract data model is proposed, with definitions and descriptions of each level presented. As an important aspect of spatial analysis, the kernel of the spatial network graph analysis is the shortest route solution. Discussions are made on classifying system of the shortest route, and illustrations are given on some classic route analysis algorithms, with improvement on the application of the algorithm studied. As for other applications of the spatial network analysis, for example, network configuration, theory and basis algorithms of network flow optimization, are also discussed, with evaluation of the efficiency of the algorithms provided.6. Taking the example of the road network graph application, the application of spatial network graph in practice: data organization of route network,map match and route analysis, is discussed, and based the application of vehicle navigation system, stressly discussed the algorithm of route analysis, an ameliorative algorithm called "virtual link" is presented. Finally some network analysis based algorithms are testified.