Network graph theory

              Incidence Matrix    

  

Incidence matrix give information about incoming and outgoing currents at a node in a circuit. before going to incidence matrix , you should clear basic terms of graph network. 

Rank of matrix is n-1.The matrix order depend upon number of branches and number of nodes present in original graph.
Order of graph depend upon number of nodes (for row) and branches /edges(for column ).

the above diagram give basic idea of incidence matrix. In incidence matrix, incoming branches are taking as negative one , outgoing branches are taking as positive one and not connected branches are taking as zero. The sum of all column are zero.

Here the another matrix comes out which is known as reduced matrix. In reduced matrix nothing is new, just one row of incidence matrix is omitted of incidence matrix . Here is an example of reduced matrix:-

The sum of column not necessary to be zero.

Advantage of reduced matrix is , it required less elements as compared to incidence matrix. Basically,reduced matrix is used to find problem in circuit.