結節地域・機能地域の分析手法

中国地方を例として

抄録

Several methods for the regionalization of nodal and functional regions and the classification of hierarchical orders of central places have been developed recently. In order to understand clearly the characteristics of each of the following five methods the writer conducted such a study by using data for telephone calls among 66×66 areas in the Chugoku District, Southwestern Japan.
The main results are summarized as follows:
(a) Direct connection method. This method has been generally used to demarcate the tributary areas of central places and to classify the hierarchical order by analysing only the nodal flows without considering the indirect flows for each place. The regionalization using this method was not satisfactory, because telephone districts as a basic unit of the analysis were often established artificially. It seems better to rank the order of each place while comparing with the central place of the highest order, Hiroshima, in the research area.
(b) Graph theory method. In this method as it was used by Nystuen and Dacey indirect flows were added to the analysis basing on the graph theory. However, some problems, like the mathematical assignment of indirect flows to each route and the indefiniteness of indirect connection, are encountered in considering the volume of total association for each area. Again, with this method as with the direct connection method, there are some problems in the hierarchical ordering of central places, because only the largest flows are utilized. However, since the analyses of both matrices B'(=Y+Y²+Y³) and B arrived at the same result, the usefulness of matrix B analysis was verified, In addition, Fig. 2 which shows the distribution of nodal regions analysed by this method, was almost the same as Fig. 1 which shows the regionalization by the direct connection method.
(c) Functional distance method. This method is used to measure the accessibility between each area by using mean first passage time (MFPT), to classify nodal and functional regions and to clarify the hierarchical structure of central places. The regionalization of nodal regions by the cluster analysis among places of origin in the matrix of MFPT is similar to that analysed by the direct connection and graph theory methods, except for a tendency toward the isolation of one or two remote rural areas from the main groups (Fig. 5). On the other hand, the hierarchical ordering of each area by the cluster analysis among places of destination in the matrix of MFPT as well as among column vectors of average MFPT did not correspond to the central place order because they do not measure the centrality of places but the accessibility itself within the research area. In addition, many of the higher order centres were integrated to one group contrary to Christaller's theory.
Moreover, since the elements of standardized column vectors of MFPT have no tendency to be extremely low to the neighbouring area of large central cities the neighbouring effect of functional distance is emphasized for the nodal regionalization using shortest functional distance and the nodal regions for large central cities tend to be delimited narrowly (Fig. 6).
(d) Factor analysis method. Factor analysis (principal axis method with varimax rotation) as well as the functional distance method extracts functional regions based on the similarity of the patterns of places of origin or destination. Since the origin-destination matrix contains many zero values it is necessary for the factor analysis to approach the normal distribution by some means of transformation. In Fig. 7, which shows the spatial distribution of areas with factor loadings over 0.5 and standardized factor scores over 1.0 for each factor within 13 factors extracted by R-method, some partial overlappings occur to functional regions of small factors.