Quantitative research on spatial morphology topology of Fujian mountain settlements by integrating graph theory algorithm and spatial syntactic analysis and GIS visualization implementation

This study takes Fujian Putian mountain settlement as the object, integrates the graph theory algorithm and spatial syntax analysis, constructs a multi-scale quantitative index system, and systematically researches the topology and functional attributes of the spatial form of the settlement by combining with GIS technology.By integrating multi-source data and extracting 782 samples of settlements, five types of quantitative indexes, namely, aspect ratio , modified shape index S, compactness W, average width of edge space L and dispersion K, are proposed, which are combined with the parameters of spatial syntax, such as integration and comprehensibility, to analyze the law of spatial differentiation of settlements.The empirical analysis shows that: the foothills and riverbanks type of clusters have the mean value of shape index up to 2.89 (S2), and the aspect ratio =2.39, which shows a significant banding feature, and the river valley and flat dam type of clusters have a larger area, such as 188,899.85m in Village V, but the shape index is medium, S=1.54.The mountain type of clusters have the lowest integration degree, with the mean value of 0.618, and the degree of spatial discretization is high.The study was visualized by GIS with linear fitting, and the goodness of fit R 0.98 revealed the strong correlation between geographic constraints and colony shape, providing data-driven theoretical support for the protection and planning of mountainous colonies.