Geography Reference
In-Depth Information
When results for all columns have been processed, move onto column 1, row 2:
ID(1,2) ¥ ID(1,1) +
ID(2,2) ¥ ID(1,2) +
ID(3,2) ¥ ID(1,3) +
…
and so on until the end of the column and row. At that point add together all the mul-
tiplied values. h is i nal value is written to cell 2,2 in the new matrix
C
2
. See Appendix
A if further examples of matrix multiplication are required.
h is process is completed for all columns and rows. h e end result is shown in
Table 6.2.
Note that in the case of, for example, connectivity between node 4 and itself, the
value of 4 in
C
2
indicates movement from node 4 to node 2, 3, 7, or 8 and back to node 4.
h e matrix for order 3,
C
3
, is obtained by multiplying the matrices
C
1
and
C
2
together.
h e number of meaningful
C
matrices is determined by the diameter of a network. h e
diameter of a network is dei ned as the maximum number of steps needed to move
from any to node to any other node in the network using the shortest possible route
(Chou, 1997). In the case of the network in Figure 6.1, the network diameter is i ve—
that is, i ve steps are necessary to move from node 1 to node 12 or node 13. h erefore,
in this case a matrix of order 5 is meaningful, but this is not the case for any higher
order. Adding the entries of each cell in each of the
C
matrices (
C
1
to
C
5
for the exam-
ple) gives the total accessibility matrix, or
T
matrix, which indicates the number of
ways to move between one node and another in a given number of steps (i ve in the
example) or less (Taafe
et al.
, 1996). Taafe
et al.
(1996) demonstrate the application of
the
T
matrix for identifying the new link that would most markedly increase the
Table 6.2
Connectivity matrix for order 2
=
matrix
C
2
ID1
2
3
4
5
6
7
8
9
10
11
12
13
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
3
0
1
2
0
0
0
1
1
0
0
0
0
0
4
1
0
0
4
1
1
0
0
1
2
1
0
0
5
0
0
0
1
1
0
0
0
1
1
0
0
0
6
0
0
0
1
0
1
0
0
0
1
1
0
0
7
0
1
1
0
0
0
4
2
0
0
0
1
1
8
0
1
1
0
0
0
2
4
0
0
0
1
1
9
0
0
0
1
1
0
0
0
1
1
0
0
0
10
0
0
0
2
1
1
0
0
1
4
1
0
0
11
0
0
0
1
0
1
0
0
0
1
1
0
0
12
0
0
0
0
0
0
1
1
0
0
0
1
1
13
0
0
0
0
0
0
1
1
0
0
0
1
1
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