We can use our adjacency matrix to count the number of ways to walk along a graph. To find the number of length \(L\) walks from \(i\) to \(j\), we have to take our matrix \(A\) and raise it to the \(L^{th}\) power, \(A^L\), and find the entry that is in the \(\left(i,j\right)\) position to find the solution. From our adjacent matrix above, we can calculate how many length \(1\) walks there are from vertices \(1\) to \(4.\) Looking at the entry for \(\left(1,4\right)\) we see a \(1.\) Thus, there is only one way to walk this path of length \(1.\)