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	0	1	0	0	0	0	= 1
N2	1	0	1	0	0	0	= 2
N3	0	1	0	1	1	0	= 3
N4	0	0	1	0	0	0	= 1
N5	0	0	1	0	0	1	= 2
N6	0	0	0	0	1	0	= 1

Accessibility Matrix (A)

C²

C³

C⁴

	N1	N2	N3	N4	N5	N6
N1	0	1	0	0	0	0
N2	1	0	1	0	0	0
N3	0	1	0	1	1	0
N4	0	0	1	0	0	0
N5	0	0	1	0	0	1
N6	0	0	0	0	1	0

	N1	N2	N3	N4	N5	N6
N1	1	0	1	0	0	0
N2	0	2	0	1	1	0
N3	1	0	3	0	0	1
N4	0	1	0	1	1	0
N5	0	1	0	1	2	0
N6	0	0	1	0	0	1

	N1	N2	N3	N4	N5	N6
N1	0	2	0	1	1	0
N2	2	0	4	0	0	1
N3	0	4	0	3	4	0
N4	1	0	3	0	0	1
N5	1	0	4	0	0	2
N6	0	1	0	1	2	0

	N1	N2	N3	N4	N5	N6
N1	2	0	4	0	0	1
N2	0	6	0	4	5	0
N3	4	0	11	0	0	4
N4	0	4	0	3	4	0
N5	0	5	0	4	6	0
N6	1	0	4	0	0	2

.
A

.
=

N1 N2 N3 N4 N5 N6 Accessibility
of a Node
S

N1| 3 3 5 1 1 1 = 14

N2| 3 8 5 5 6 1 = 28

N3| 5 5 14 4 5 5 = 38

N4| 1 5 4 4 5 1 = 20

N5| 1 6 5 5 8 3 = 28

N6| 1 1 5 1 3 3 = 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