Abstract
Interaction data between nodes are usually presented as an interaction matrix to facilitate understanding and analysis of interaction. Temporal changes of an element or a part of an interaction matrix may be easily discerned, but overall changes of the matrix are often difficult to grasp. Such a difficulty is commonly encountered in investigation of a regional system, which is constructed on the basis of interaction data. In this paper, Medvedkov's method of settlememt pattern analysis (1967) is adapted to measure randomness of linkages and organizing potential for nodal regions associated with the randomness in the 1959 and 1965 United States air networks, whosee nodes consist of the 100 largest cities in terms of air passenger generation.
Medvedkov developed a method incorporating Shannon's entropic measure Hs in the method to separate the random and uniform components in an actual lattice of settlements. It is supposed that the actual lattice consists of two lattices, the random and uniform ones. In his method, Hs is calculated first, and the value is used to estimate the random component. In the present paper the same method was applied to the air connection matrices to sepa-rate the random and uniform components. The actual connection matrix is assumed to be composed of the random and uniform matrices. When the air network consists of only the uniform component, the network is undifferentiated and it does not have organizing potential for nodal regions at all. Hence, the regionalization potential of the netwrok can be attributed only to the other component of the actual matrix, the random matrix. When the air network is defined as an open system, the change of the total connection value B (Table 3) can be considered as arising from the external causes, which are multifactorial and rather complex. For this reason, it is more useful to compare the random and uniform components by their ratios within the system. The greater the random ratio, the greater the regionalization potential. As the random ratio declines in the connection matrix, the regionalization potential decreases, and the network division becomes more difficult.
From 1959 to 1965, the total connection value increased from 11, 536 to 16, 422 (Table 3). With the increase of B the random component also increased, but the ratio of the random component decreased 1.5% from 13% to 11.5% because the uniform component increased more rapidly than the random one. From the viewpoint of the entropic measure presented in this paper, the intensification of nodal fields associated with the increase of linkages in the air network resulted in the relative decline of regionalization potential in the system.
The adaptation of Medvedkov's method in this paper is more specialized than the use of Hs or relative entropy (Hs/Hmax) alone as a means of analyzing regionalization potential from the geographer's viewpoint. The association of the random component of the connec-tion matrix with the regionalization potential of the matrix is conceptually interesting. This somewhat specialized use of entropy, however, is not without cost, since the method cannot be applied to matrices with the average values per cell of 1.0 or less, at least, with its present equation (3) for the approximation of the random component. Despite this short-coming of specialization, incorporation of other geographic variables such as distance and node size into the entropic model seems desirable.
