graph theory in network analysis by deep nandi

1. BY DEEP NANDI
BRANCH:- EE(2nd year)
ROLL NO.- 31

2. When all the elements (e.g. R, L,C)
in a network are replaced by lines
with circles or dots at both ends the
configuration is called graph of the
network.

3.  BRANCH
 NODE
 TREE
 TREE LINK
 TREE BRANCH
 LOOP
 MATRIX

4. : A branch is a line segment representing one
network element or a combination of element
connected between two points.
: A node point is defined as an end point of
a line segment and exist at the junction between two
branches.
: It is an inter connected open set of branches
which include all the nodes of given graph.

5. 1
2
3

6. PROPERTIES OF TREE
 It consist of all the nodes of the graph .
 If the graph has n number of nodes the tree will n-1
number of branches
 There will be no closed path in the tree .
 There can be many possible different for a given graph
depending on the number of nodes and branches.

8. INCIDENCE MATRIX
 Row -> node , column -> branch
 Algebraic sum of column entries of an incidence matrix
is zero.
 Determinant of incidence matrix of a closed loop is
zero .
1 2 3
1 2
4
3
5

9. Row -> cut-set , column -> branch
Draw the tree of the graph .
Take the direction of cut-set as the twig
direction .
The direction along the branch of cut-set
is taken as positive one and if the
direction is opposite it is taken as
negative one .

10. 1 2 3
4
3
5
4
6
2
1

11.  R0w -> loop current , column -> branches
 Draw the tree from the given graph
 Take the direction of loop as a link direction.
 The branch having the same direction as a loop
direction is taken as 1 and if opposite direction it is
taken -1.

12. 1
2 3
4
1 2
3
4 5I

13.  Relation between twig and link L=B-N+1
 If the graph as N number of nodes , tree will have N-1
branches.
 Number of trees of a graph T = determinant [A].[A]^t
 Orthogonal relationship [A].[B]^t =0 or [B][A]^t = 0
 [Vb] = [Q]^t .[Vt]
 [Vb] = [A]^t[Vn]