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Matrix Analysis of Networks

(http://faculty.washington.edu/krumme/systems/networkmatrix.html)


Supporting  &   Related   Pages:


Network (Graph)

N1-------------------- N2-------------------- N3-------------------- N5-------------------- N6
. |
. |
. |
. |
. |
. |
N4

Network Diameter = 4



Connectivity Matrix (C)

N1 N2 N3 N4 N5 N6 Nodal
Degree
S
N1 010000 = 1
N2 101000 = 2
N3 010110 = 3
N4 001000 = 1
N5 001001 = 2
N6 000010 = 1


Accessibility Matrix (A)

C

+
C2

+
C3

+
C4

N1 N2 N3 N4 N5 N6
N1 010000
N2 101000
N3 010110
N4 001000
N5 001001
N6 000010
+
N1 N2 N3 N4 N5 N6
N1 101000
N2 020110
N3 103001
N4 010110
N5 010120
N6 001001
+
N1 N2 N3 N4 N5 N6
N1 020110
N2 204001
N3 040340
N4 103001
N5 104002
N6 010120
+
N1 N2 N3 N4 N5 N6
N1 204001
N2 060450
N3 4011004
N4 040340
N5 050460
N6 104002


.
A

.
=

N1 N2 N3 N4 N5 N6 Accessibility
of a Node
S
N1| 335111 = 14
N2| 385561 = 28
N3| 5514455 = 38
N4| 154451 = 20
N5| 165583 = 28
N6| 115133 = 14


Q =

How does the accessibility of the 6 nodes change as a result of the intruction of a new (direct) link between N4 and N6? Recalculate the A matrix and briefly interpret your results.

Source: Taaffee & Gauthier, Geography of Transportation, 1973, Ch.5


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2003 [econgeog@u.washington.edu]