Cut-set matrix: It gives the relation between cut-set voltages and branch voltages. The rows of a matrix represent the cut-set voltages. The columns of a matrix represent the branches of the graph. The order of the cut set matrix is (n – 1) × b. The rank of a cut-set matrix is (n – 1) The elements of a cut set matrix, = n−1×b = +1, if jth branch is incident to ith cut set and oriented in same direction = –1, if jth branch is incident to ith cut set oriented in opposite direction = 0, if jth branch is not incident with ith cut set voltage. Example: Let the graph is = 0 Where is the column matrix of branch currents. We can express the branch voltages in terms of tree branch voltages or twig voltages, using the cut-set matrix Q. = T Where, Vb is the column matrix of branch voltages Vt is the column of matrix of twig voltages Now, from the above matrix, it is clear that, The submatrix corresponding to twigs (Qt)­ is an identity matrix The submatrix corresponding to links (Ql)­ is not an identity matrix, it is a rectangular matrix. The rank of tie set matrix is (n – 1) i.e. 3 for the above matrix