If we want to represent a relation between number of link current and number of branch currents in a directional graph, we should use:  

Tie set matrix:

• It gives the relation between tie-set currents and branch currents.
• The rows of a matrix represent the tie-set currents.
• The columns of a matrix represent branches of the graph.
• The order of the tie set matrix is (B – N + 1) × b
• The rank of a tie-set matrix is (B – N + 1)

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)

Incidence matrix:

• It is the matrix which gives relation between branches and nodes.
• The rows of matrix represent the number of nodes and the columns of matrix represents the numbers of branches.
• We can construct the incidence matrix for the directed graph. We can draw a graph with the help of incidence matrix.
• The algebraic sum of elements of all the columns is zero.
• The rank of incidence matrix is (n–1).
• The order of  incidence matrix will be (n × b).
• The determinant of the incidence matrix of a closed loop is zero.

Reduced incidence matrix:

• If one of the nodes in the given graph is considered as reference node, then that row can be neglected by writing incidence matrix is called as reduced incidence matrix.
• The order of reduced incidence matrix is (n–1) × b.
• The Algebraic sum of some of the columns is not zero.