1. Gujarat Power Engg. & Research Institute(104)
Topic : Network topology
Guided By: Prof. Ashvin patel
Sub: Circuit and Network( )
BE Electrical (Sem-3)
Prepared By:-
Patel Dhaval P. ( )
Patel Nirav G. ( )
Patel Dhaval A. ( )
Patel Bhavit B. ( )

2. Index
Network Graphs
Matrix

3. Network graphs

4. A Graph is a collection of nodes and branches .
The nodes are join together by branches .
Types of Network graphs :-
- Planar graph
- Non planar graph
- sub graph
- Path
- connected graph
- tree
- co –tree
- fundamental loop
- Rank
- loop
- cut set

5. Graph:-
A graph show in geometrical interconnection of the element of a network.
PLANAR GRAPH
A Graph drawn on a two dimensional plane is said to be planar ,if two branches do not interact of cross at a point which is other than node.

6. NON PLANAR GRAPH
A graph drawn on a two dimensional plane is said to be non planar , if there is intersection of two or more branches at another point which is not a node.

7. Oriented graph:
In a graph if each element of a connected graph is assign a direction than its known as oriented graph

8. Example of Oriented graph for this circuit:6 4 5 1 2 3

9. SUB-GRAPH A sub graph is a sub set of branches and node of graph.
A sub graph is said to be proper sub graph, if it has number of nodes and branches strictly less than that of the original graph.
A sub graph can be just a node or only one branch of a original shown in figure…

10. (a)Graph (b)Sub-graph2 3 4
(a)Graph (b)Sub-graph

11. Path
It is an proper sub graph consisting of an ordered sequence of a branches having the following properties:
(a) At two of its nodes called terminal nodes, there is incident only one branch of the sub graph.
(b)At all remaining nodes called internal nodes, there are incident two branches of graph. 2 3 4
path

12. Connected Graph: Rank:
- A graph said to be connected if there exists a path between any pair of nodes , otherwise a graph is disconnected . the having a transformer as one of the element is an unconnected or disconnected.
Rank:
- If there are ‘n’ nodes in a graph , the rank of the graph is (n-1)

13. Loop
It is sub graph of graph where in at each node exactly two branches are incident. If two terminals of a path are made to coincide, it will result in a loop or a circuit.

14. Fundamental loop
Loop which contains only one link is called fundamental loop. Such loops are independent and are called basic or F.loops or tie sets.
Cousequently the number of F.loops is equal to the number of links. 2 1 G 3 F E
Here F,E,G are loops

15. Tree
A tree is connected subgraph of a connected graph having all the nodes of the graph but without any loop. Branches of a tree is called twings.a tree contains (n-1)twings where n is number of nodes in a graph. 3 1 2 4
(b)tree
(a)Graph

16. Co-tree
Branches which are not on a tree is call links or chords.since these branches are the complement of twings they constitute what is known as co-tree.
Since a tree has a all the nodes of the graph,the numbers of branches in the tree is one less than the numbers of the nodes. i.e.
IF the numbers of nodes = n
The number of twings in tree=(n-1)
Suppose the total number of branch in graph= b;
The number of links in co-tree= b-(n-1).

17. 2 1 3 4
(b)Co-tree
(a)Graph

18. matrices

19. Element node incidence matrix6 4 5
ELE NODE 1 2 3 4 5 6 -1 1 2 3
Matrix

20. Bus incidence matrix
In element node incidence matrix, if we remove reference node’s row than we get matrix called bus incidence matrix.
For given circuit:-1, bus incidence matrix is given below:-
ELE NODE 1 2 3 4 5 6 -1

21. Cut set
Consider a linear graph by removing the set of branches without affecting the nodes to connected sub graphs are obtain and the original graph becomes unconnected. The removal of this set of branches which results in a cutting the graph into two parts is known as cut set.

22. Cut Set matrix 6 4 5 2
Ele
cuts 1 2 3 4 5 6 A -1 B C 1 3 C A B 2 3 1 4

23. Fundamental Tie-Set Matrix
The incidence of element to basic loops of connected graph is shown by basic loops incidence matrix.
Example:- for a circuit-1 2 1 G 3 F E 4

24. Example for tie-set matrix6
Ele
loop 1 2 3 4 5 6 7 E -1 F G 4 2 5 1 G 3 F E 1 2 3 4

25. Thank you…