Homogeneous groups

Meanwhile for all provinces we can compute the elements of a distance matrix D which
represents the composite distances as measured by m indicators.

1

21

, for p=1, 2, ..., n; and q=1, 2, ..., n (3)

Every element of matrix D is a mathematical expression of several distances (as many as the
number of indicators) between two provinces of p and q. This matrix is presented in Table B2 in
Appendix B. Across every row of this matrix the minimum non-zero value shows the shortest
distance between two closest provinces represented by the respective row and column. Every
province can be connected to its closest neighbour by means of an arrow. This will result in a
set of disconnected sub-sets of first order graphs which represent the first order homogeneous
provinces in close neighbourhood. Second order connections may be determined in the same
way. Links with values above a certain critical value may be regarded as too far to indicate
close neighbourhood. Similarly distances below a lower bound indicate almost identical
provinces. These critical upper and lower values are represented by d₍₊₎ and d_(-) and are found
as follows:

d₍₊₎ = d+2s_d
d(-) = d^_ -2sd

where d and s_d are the mean and standard deviation of all minimum distances belonging to n
provinces.¹² The upper bound d(+) may be regarded as the critical minimum distance. If the
composite distance between two provinces falls below this value these two provinces may be
regarded to be in the neighbourhood of each other that is they are members of a homogenous
group. All links with a length greater than the value of this upper bound may be removed
since they are too long to be part of a single graph. Theoretically any composite distance value
below d(-) indicates that the two provinces are practically similar. Table B2 in Appendix B
shows the interregional distances and the neighbour of each province along with the critical
distances of d(+) and d(-).

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