What are the property of INCIDENCE matrix? Why we used it in Network analysis?

• INCIDENCE MATRIX:-

➝ "Incidence matrix is the mathematical representation of node current and voltage in various branches of the network".

➝Incidence matrix is used to describe the Nature of Incoming and Outgoing branches across any nodes in the Network.

➝Order of Incidence matrix is;

                 [A]n×B.    

           Where; n = Numbers of node

                          B = Number of branches 

• HOW TO MAKE INCIDENCE MATRIX OF GRAPH:-

Fig(a) GRAPH OF NETWORK

• Before making Incidence matrix of any graph following points are keep in mind.

⇨ +1 = If Direction of current is Away from node.
⇨ -1  = If Direction of current is Towards the node.

⇨ 0   =  If note Incidence 

• Now select any one node and check direction of current in all branches of the network corresponding to this particular node.
• Suppose we consider Node "A" please observed in fig (a) direction of current in branch 1 is towards the node so it is -1, and direction of current in branch 2 & 6 is away from the node so it is +1 and finally branch 3,4&5 are not Incidence so it is 0.
• All this steps are perform by taking one by one nodes.
• Finally we get Incidence matrix as shown in below figure.

Fig(b) INCIDENCE MATRIX OF GIVEN GRAPH 

✱PROPERTY OF INCIDENCE MATRIX:-

➝ Summation of all the columns of Incidence matrix is equal to ZERO.

➝ If the network ha Number of nodes is equal to numbers of branches (n = B) then the resultant Incidence matrix is a SQUARE MATRIX.

➝ The determinants of square matrix is always ZERO.

" INCIDENCE MATRIX IS USED TO FIND THE POSSIBLE TREES OF ANY NETWORKS WITHOUT DROWNING IT".

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