As homework, I had to construct an adjacency matrix for the following graph:
My solution was the following:
$$ \begin{bmatrix} 0&0&1&0&0 \\ 1&0&0&1&0 \\ 0&1&0&1&0 \\ 0&0&0&0&0 \\ 1&0&1&0&0 \end{bmatrix} $$
That means:
- vertex v1 shows to v3
- v2 shows to v1 and v4
- etc.
However, the correct solution was the following adjacency matrix:
$$ \begin{bmatrix} 0&1&0&0&1 \\ 0&0&1&0&0 \\ 1&0&0&0&1 \\ 0&1&1&0&0 \\ 0&0&0&0&0 \end{bmatrix} $$
So, the transpose of my matrix is the correct solution. Unfortunately, I can't reach my lecturer over the weekend.
Could anyone please explain why my answer is wrong?
PS: When you enter the following string into wolframalpha.com 1->3, 2->1, 2->4, 3->2, 3->4 ,5->1 ,5->3 directed graph, you get the graph above, which is basically my matrix.