Electric Circuits and Networks, Ist Edition by Pearson

Topological

properties of a

network.

i

1

i

2

i

3

i

4

i

5

i

6

v

1

v

2

v

3

v

4

v

6

v

5

A

B

D

(b)

C

+

+

+

–

–

–

+

–

+

–

+

–

i

1

i

2

i

3

i

4

i

5

i

6

v

1

v

2

v

3

v

4

v

6

v

5

A

B

D

(a)

C

+

+

+

+

+

+

–

–

–

–

–

–

i

1

i

2

i

3

i

4

i

5

i

6

v

1

v

2

v

3

v

4

v

6

v

5

A

B

(c)

C

D

+

+

–

–

+

–

+

–

+

–

+

–

Fig. 17.1-1 Three Electrical Networks with the Same Network Structure

However, the KCL equations written for the four nodes and the KVL equations

written for the six loops will be identical for the three networks. They are:

ii

iiii

ii

iiii

vvv

vv

12

3452

65

1346

123

34

0

0

0

0

0

+=

++−=

−=

−− − − =

−+ + =

−+ ==

−++ =

−+ + + =

−+ + =

−+ + =

0

0

0

0

0

456

1256

124

356

vvv

vvvv

vvv

vvv

The study of topological properties of a network employing a branch of Mathematics

called Linear Graph Theory is termed Network Topology. This ...