I am trying to understand why Random Walks' and Random Jumps', on a graph, transition matrix are also stochastic matrix.
A stochastic matrix is a matrix the values of each row add up to 1 and no value is < 0.
I am trying to understand why Random Walks' and Random Jumps', on a graph, transition matrix are also stochastic matrix.
A stochastic matrix is a matrix the values of each row add up to 1 and no value is < 0.
The $(i,j)$th entry of the transition matrix is the probability that on any given step, starting from vertex $i$, you will pass to vertex $j$. So the sum of the values in the $i$th row represents the probability that, on a given step, you will pass to vertex 1, or to vertex 2, or to vertex 3, etc. -- this probability is 1, since you must end up at one of the vertices. The entries are nonnegative since probabilities are numbers between 0 and 1 (inclusive).