Electrical Circuits EEE Properties of incidence matrix: 1. Number of non zero entries of row indicates degree of the node.
2. The non zero entries of the column represents branch connections.
3. If two columns has same entries then they are in parallel.
Procedure to form incidence matrix: aij = 1, if jth branch is incidence to ith node and direction is away from node.
aij = -1, if jth branch is incidence to ith node and direction is towards from node.
aij = 0, if jth branch is not incidence to ith node .
Example: Draw incidence matrix for the given graph.
Solution: In the above shown graph or directed graph, there are 4 nodes and 6 branches. Thus
the incidence matrix for the above graph will have 4 rows and 6 columns.
For the graph shown above write its incidence matrix.
Reduced Incidence Matrix: If from a given incidence matrix [A
C
], any arbitrary row is deleted, then the new matrix formed
will be reduced incidence matrix. It is represented by symbol [A]. The order of reduced
incidence matrix is (n-1)*b where n is the number of nodes and b is the number of branches
.
Malla Reddy College of Engineering and Technology (MRCET)
Department of EEE ( 2017-18 )
Electrical Circuits EEE [
NOTE : In the above shown matrix row 4 is deleted.]
Tie-set: It is a unique set with respect to a given tree of a connected graph containing one chord
and all of the free branches contained in the free path formed between two vertices of the chord.
