Another important matrix is the transition matrix. A transition matrix also denoted as \(P\), is a matrix that shows random walks and its probabilities for each step. The way to read the probability between vertices is \(P_{ij}\) where \(i\) and \(j\) are the row and column respectively. The transition matrix can also be done for different lengths \(L\). To do this we take our transition matrix \(P\) and raise it to the \(L\) power.