× Home MCQ Videos Basic Electrical Circuit Theories Electrical Laws Materials Batteries Illumination Generation Transmission Distribution Switchgear Protection Measurement Control System Utilities Safety Transformer Motor Generator Electrical Drives Electronics Devices Power Electronics Digital Electronics Biomedical Instrumentation

What is Incidence Matrix?

Incidence matrix is that matrix which represents the graph such that with the help of that matrix we can draw a graph. This matrix can be denoted as [AC] As in every matrix, there are also rows and columns in incidence matrix [AC].
The rows of the matrix [AC] represent the number of nodes and the column of the matrix [AC] represent the number of branches in the given graph. If there are ‘n’ number of rows in a given incidence matrix, that means in a graph there are ‘n’ number of nodes. Similarly, if there are ‘m’ number of columns in that given incidence matrix, that means in that graph there are ‘m’ number of branches. incidence matrix

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. The entries of incidence matrix is always -1, 0, +1. This matrix is always analogous to KCL (Krichoff Current Law). Thus from KCL we can derive that,

Type of branchValue
Outgoing branch from kth node+1
Incoming branch to kth node-1
Others0

You may also be interested on
What is Incidence Matrix?

Steps to Construct Incidence Matrix

Following are the steps to draw the incidence matrix :-
  1. If a given kth node has outgoing branch, then we will write +1.
  2. If a given kth node has incoming branch, then we will write -1.
  3. Rest other branches will be considered 0.

Examples of Incidence Matrix

incidence matrix

For the graph shown above write its incidence matrix. incidence matrix

Reduced Incidence Matrix

If from a given incidence matrix [AC], 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. For the above shown graph, the reduced incidence matrix will be :- reduced incidence matrix [NOTE :- In the above shown matrix row 4 is deleted.] Now let us consider a new example related to reduced incidence matrix. For the graph shown above write its reduced incidence matrix. directed graph Answer:- In order to draw reduced incidence matrix first of all draw its incidence matrix. Its incidence matrix is :- Now drawing its reduced incidence matrix. For this we just simply have to delete any node (in this we have deleted node 2). Its reduced incidence matrix is:- This is the required answer. Points to remember


AADITYA commented on 25/04/2018
Detailed explanation. Thank you so much.
Comments


New Articles
Indoor SwitchgearEEG MeasurementElectroencephalography | EEGECG Recording SetupElectrocardiography
Articles on Matrix
Trees and CotreesIncident MatrixCutset Matrix
More Articles on Circuit Theory
Circuit and NetworkCircuit TheoremCircuit AnalysisTwo Port NetworkOp-ampRLC Circuit
Articles Categories
MCQ Videos Basic Electrical Circuit Theories Electrical Laws Materials Batteries Illumination Generation Transmission Distribution Switchgear Protection Measurement Biomedical Instrumentation Control System Utilities Safety Transformer Motor Generator Electrical Drives Electronics Devices Power Electronics Digital Electronics Guest Post