17.2 THE INCIDENCE MATRIX OF A LINEAR ORIENTED GRAPH
A linear oriented graph can be described in graphical form as in Fig. 17.2-1. It can also be described in tabular form with the branch number ‒ starting node for that branch and ending node for that branch as entries in the rows of the table. The same information can be given in the form of a matrix called All Incidence Matrix Aa defined as below.
The All Incidence Matrix Aa of an oriented linear graph has as many rows, as there are nodes in the graph. It has as many columns, as there are branches in the graph. Let aij represent the entry in Aa at ith row-jth column position. Then,
aij = 1, if the jth branch is incident at the ith node and is oriented away from that node.
= – 1, if the ...