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Consider the following statements regarding the complete incidence matrix (A) of order n × b (a) The elements aij of A = 1, if branch j is associated with node i and orientation is towards node i (b) The element aij of A = -1, if the branch j is the cut set i and the orientation coincide (c) The element aij of A = 1­, if the branch j is associated with node i and orientation is away from node i (d) The element aij of A = 0, if the branch j is not associated with node i Which of the above statements are correct?

Consider the following statements regarding the complete incidence matrix (A) of order n × b (a) The elements aij of A = 1, if branch j is associated with node i and orientation is towards node i (b) The element aij of A = -1, if the branch j is the cut set i and the orientation coincide (c) The element aij of A = 1­, if the branch j is associated with node i and orientation is away from node i (d) The element aij of A = 0, if the branch j is not associated with node i Which of the above statements are correct? Correct Answer c and d

  • The incidence matrix (A) is a mathematical model to represent the given network with all information.
  • The rows of the incidence matrix represents the number of nodes and the column of the matrix represents 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 ‘b’ number of columns in that given incidence matrix, that means in that graph there are ‘b’ number of branches.

The standard convections for incidence matrix are:

aij = 1, if branch j is associated with node i and is oriented away from the node i

ajj = -1, if branch j is associated with the node i and is oriented towards node i

ajj = 0 if branch j is not associated with node i

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