Gujarat Power Engg. & Research
Institute(104)
TOPIC :
NETWORK TOPOLOGY
GUIDED BY: PROF. ASHVIN PATEL
SUB: CIRCUIT AND NETWORK(2130901)
BE ELECTRICAL (SEM-3)
PREPARED BY:PATEL DHAVAL P. (131040109027)
PATEL NIRAV G.
(131040109036)
PATEL DHAVAL A. (131040109026)
PATEL BHAVIT B.
(131040109025)
Index
 Network
 Matrix
Graphs
Network graphs


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
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.
• 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.
• Oriented graph:
•
In a graph if each element of a
connected graph is assign a direction
than its known as oriented graph
Example of Oriented graph for this
circuit:
Circuit :-1
6
5
4
2
3
• 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…
2
3
4
(a)Graph
(b)Sub-graph
• 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
•
Connected Graph:
- 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)
• 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.
• 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
F
E
G
Here F,E,G are loops
3
• 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.
1
(a)Graph
3
2
4
(b)tree
• 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).
1
2
3
4
(a)Graph
(b)Co-tree
matrices
• Element node incidence
matrix
6
5
4
ELE
NODE
1
2
3
2
3
1
2
3
-1
4
5
1
-1
6
1
-1
1
Matrix
1
-1
• 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
1
2
3
-1
4
5
1
-1
6
1
-1
1
1
-1
• 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.
• Cut Set matrix
6
4
1
A
5
2
B
2
4
3
C
Ele 1
cuts
A
B
3
C
2
3
1
4
5
-1
1
1
1
6
-1
1
1
-1
• 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
F
E
4
G
3
• Example for tie-set
matrix
6
1
4
2
5
F
G
E
2
4
3
3
Ele 1 2
loop
3
4
5
E
1 -1
-1
-1
1
F
-1
G
1
6
7
1
-1
1
Thank you…