为了克服首位度分析的简单化，避免位序‐规模模式的不可比性，选取国家最大城市人口规模（ P）、城市首位比（R）和城镇等级体系不平衡指数（S）3个指标来分析国家城市等级体系的世界格局。首先将156个国家的城市人口分为10～25万、25～50万、50～100万、100～500万以及500万以上5个等级，计算出城镇等级体系不平衡指数（S）和城市首位比（R），剔除 S＝1的31个国家，然后对 P ，R和 S 采用系统聚类法（Hierarchical cluster ）和自组织映射法（SOFM ）来揭示国家城市等级体系的世界格局。结果表明，国家城市等级体系的空间格局可以分成6大类型：高级‐中级平衡型、中级平衡型、初级平衡型、初‐中级不平衡型、初级不平衡型和初级首位型。分类结果说明利用自组织特征映射法（SOFM ）对国家城市等级体系进行分类，分类效果较好，可以反映城市等级体系国家间的异同。%In order to overcome the simplicity of the primacy index and the incommensurability of the rank‐size model , this paper selects unbalanced index of the urban hierarchy system (S) , the population of the largestcity(P)andurbanprimacyratio(R)tostudytheworldpatternofnationalurbanhierarchysystem . On this basis , firstly the 156 national city population is divided into 10~25 million , 25~50 million , 50~100 million ,100 ~ 500 million , more than 500 million of 5 grade , calculating unbalanced index of the urban hierarchy system (S) and city primacy ratio (R) , removing 31 countries of S= 1 , at last using hierarchical cluster and SOFM to reveal the world pattern of national urban hierarchy system . The result shos , that the world pattern of national urban hierarchy system can be divided into 6 types :the higher‐medium grade balance , the medium grade balance , the primary grade balance , the primary‐medium grade unbalance , the primary grade unbalance and the primary primacy . Classification results show that the classification effect is good , and it can reflect the similarities and differences between the nations using .
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