Draw the incidence matrix of the following graph.
In the incidence matrix column represents branches, while rows represent nodes. Therefore,
Note: In matrix A with n rows and b columns, an entry a_{i j} \text { in the } i^{\text {th }} \text { row and } j^{\text {th }} column has the following values:
a_{i j}=1, \text { if } j^{\text {th }} branch is incident to and oriented away from the i^{th} node.
a_{i j}=-1, \text { if } j^{\text {th }} branch is incident to and oriented towards i^{\text {th }} node.
a_{i j}=0 \text {, if } j^{\text {th }} branch is not incident to the i^{\text {th }} node.
Branches | ||||||
Nodes | a | b | c | d | e | f |
1 | 1 | 0 | 1 | 0 | 0 | 1 |
2 | -1 | -1 | 0 | 1 | 0 | 0 |
3 | 0 | 1 | 0 | 0 | 1 | -1 |
4 | 0 | 0 | -1 | -1 | -1 | 0 |