Coupon Accepted Successfully!


Definitions Related To Graph Of A Network

Loop : It is the closed contour selected in the graph.

Cut-set :
 It is that set of elements or branches of a graph that separates two main parts of a network. If any branch of the cut-set is not removed, the network remains connected.

Tree and Co-tree :
 Tree is an interconnected open set of branches which include all the nodes of the given graph. In a tree of a graph there cannot be any closed loop. A branch of tree is known as twig. Those branches of a graph which are not included a tree are called co-tree. The branches of a co-tree are called links or chords.

Total no. of links L = B – (N – 1) = B – N + 1

where B = total no. of branches

N = no. of Nodes

N – 1 = total no. of tree branches

Number of independent KCL equations = N – 1

Planar graph :
 It is drawn on a two-dimensional plane so that no two branches intersect at a point which is not a node.


Fig. : Planar graph

Non-planar graph : 
It is drawn on a two dimensional plane such that two or more branches intersect at a point other than node on a graph.


Fig. : Non-planar graph

Rank of a graph.

If there exists N number of nodes, then rank R of a graph is given by the relation

R = (N – 1)

Reduced Incidence Matrix

When one row is removed from the complete incidence matrix, the remaining matrix is called reduced incidence matrix.

If [A] is the reduced incidence matrix and [At] is the transposed matrix of [A] then, the number of possible trees of a graph

T = Determinant [A] [At]

Fundamental Cut-Set

No. of fundamental cut-sets = no. of twigs = (N – 1)

where N = no. of nodes of a graph

Number of independent node equations (n) = J(no. of junctions) – 1.

Number of independent mesh equations (m) = b (no. of branches) – (j – 1)

Test Your Skills Now!
Take a Quiz now
Reviewer Name