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Spatial functional analysis of the Greek settlements system

• Κουσιδώνης, Χρήστος, Θ.

This study is concerned with the functional regionalization of the Greek geographical space. 1.1. To begin with, the systemic nature of the concept of functional region is noticed. Further on, and from a structutalistic point of view, attention is drawn to the critical importance of the nature of the flows, or relations, used in delineating a functional region. Different kinds of flows (money, people, etc.) define, in principle, different levels of analysis, pertinent to different sciences (monetary flows are pertinent to regional economic artalysic, etc.).The regionalizations arrived at by using various kinds of flows between the same set of spatial units are not apriori identical. What is stronglyemphasized is the importance of functional regionalization for regional planning. 1.2. The flows of people between settlements are, basically, the result of the uneven distribution of the various uses of space, usually referred to as «activities» (retailing, manufacturing, recreation, etc). This implies that the flows of people are pertinent to the study of the organization of space from a functional point of view, namely the utilization of space as such, by the people as physical (-social) beings. Fallowing Λαγόπουλος (1973, 1980), whose approach to the analysis of space is* closely related to Philbrick's (1957), we call this level of spatial analysis «functional» or «spatial functional level». 2. The main data available are passenger flows between ninety-three of the largest settlements of Greece, for the year 1978. These data, summarized in a symmetrical matrix A, include: (a) the train passengers, and (b) the passengers on the bus line organization that viriually covers the whole Greek geographical space. It is accepted that A is a satisfactory approximation to the structure of functionally organized space. 3. Usually, if not exclusively, the absolute value of the flow is used as index of the relation between the spatial units. It is argued that the absolute value of the flow is not a direct index of the magnitude, or the intensity, of the relation this flow is simply bearing. A certain flow, say 10,000 persons per year, implies a strong relation when connecting two small settlements of, say, 2,000 population each, and a much weaker one when connecting two big cities of, say, 200,000 population each. It follows that: (1 ) The index of relation must be a function of the flow, but in reference to some frame wider than that of the flow matrix. To introduce a reference frame means to adopt a «denominator». (2)This denominator is to be a function of one or more variables. These variables must belong to the analytical level pertinent to the analysis of functionally organized space. The denominator, as an index in itself, must be of such a generality as the flows. It seems very reasonable to adopt as variable(s) of the denominator the population size(s). (3) The last stage in defining the index of the intensity of the relation is to decide on the exact formula of the denominator and the index as a whole. This study, due to the data available, deals with non-directed flows. Therefore it was decided to introduce into the denominator the population of both the settlements related by the flow. The adopted index is the following: ßij= Oii/(pi + ρ,)"2 where au element of matrix A, and p., p, the related settlement populations. Besides matrix B=(ßj), we wilf also deal with matrix A. This will allow interesting comparisons between the regionalizations based on the two different indices. 4. Two regionalizations procedures are used in this study: A factor analytic one, namely principal components analysis followed by Varimax rotation, and a clustering one. The latter is based on the «fine ^clustering» or «Βκ- clustering» of Jardine & Sibson (1970), also known as the «Jardine & Sibson method». In terms of graph theory this technique is as fallows (Röhlf, 1974): Let a symmetrical flow matrix (cu) be considered as the adjacency matrix of a valued graph G. M I is a given number and ois replaced by ój,cn=1 if c o I, cii=0 if Oi< I, a new matrix CI=(CÜ) is obtained and a new non-valued and non-directed graphe Gì, having the same vertices as G, corresponds to Ο. Number I is called «level» or «threshold». In Gr all the maximal complete subgraphs, Called «cliques», can be located. Let k be an integer. For any pair of overlapping cliques the number of the common vertices is noticed. If this number is at least equal to k, the missing links between the vertices of the two corresponding cliques are «restored». In this way a new graph G,,, with new, larger, cliques is obtained. G^, is subjected to the process applied to Gi.Xhe repetitions continue until no new clique is obtained. If G,,n is the graph in which no new clique can be obtained,the cliquesinG,,n are the clusters identified by the method for the given I and k. In order to pass from clustering to regionalization, some additional steps in Gì are taken, the major of which concerns the delineation of nodal regions. The*clustering regionalization procedure is of great flexibility since it is based on two parameters (I and k) the values of which can be fixed according to the characteristics of any specific application. The regionalizations produced consist of overlapping regions of densely felated spatial units. The density of the relations internal to each region and the oVerlappings contribute to the (sub-)systemic character of the regions revealed. As far as the factor analytic appoach is concerned, we hold that the process of factor analyzing offers no guarantee that the regions revealed will be spatial (sub-)systems. On these grounds we prefer to talk of «regional schemes», and not of regions, when using factor analysis. These schemes though, cbuld be of great importance in grasping the organization of spatial structure as a whole, and this is the reason why the factor analytic procedure is used in this study. 5. The results of the factor analysis of matrices A and Β are shown on maps 1 and 2, respectively. Clustering regionalizations based on matrices A and Β are showh on maps 3 and 4-5, respectively. It is noticed that factor analytic procedure has the tendency to directly display the nodal organization forms. This is not to denote that the clustering procedure conseals the nodal function of the settlements really functioning this way; it simply does not display the nodal forms as directly and in such extend as the factor analytic procedure does. The clustering procedure, as already noticed, has its empasis in locating the dense, subsystem-like, forms of spatial organization. A significant differentiation, function of the index of dyadic interaction is also noticed. The new index, ßu gives regions that are more solid in geographical terms, have more internal relations, have sizes of less diversity and are less overlapping each other. 6. The selection of the «best» regionalization, shown on map 6, is based on three criteria: (a) The regions must have a «local» character and sizes satisfying the, empirically derived, notion of regions' sizes, (b) the region must have small overlappings and (c) they must cover the whole, or almost the whole, geographical space. 7. The spatial functional level, wnile retaining a certain degree of autonomy, is articulated to any other level of the analysis of the social formation. The most influential level is the basic socio-economic organization. To comprehent the specific form of the articulation of the spatiai level to the entire socio-economic formation, constitutes the most complete interpretation of the organization of the spatial functional level. In order to go on to an approach to the articulation of the spatial functional level to the history of the socio-economic formation, a commentary is given on the way in which the «city-countryside contradiction», spatial expression of the social division of labour, manifests itself in more technical geographical terms in the system of spatial polarizations (i.e. nodal regional forms) inherent in the system of the interurban flows or persons. There follows an examination of the specific forms taken by the hierarchy of poles and polarizations within the Greek functionally organized space. It is noticed that the specialization of a settlement in some urban function(s) is more important in the interpretation of its intraregional rather, than interregional, role.

• Sociology

• Κοινωνικές επιστήμες

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